Is symmetry the key?
It seems that it is meaningless to talk about an absolute measure on the ensembles for the multiverse. However, we can make real progress by simply appealing to principles of symmetry. For example, when an atom emits a photon it seems reasonable to assume there is 50/50 chance of measuring up versus down. How could it be anything but 50/50? This is a statement about real, absolute probabilities of outcomes without any need to derive the result from some underlying measure on the infinite ensembles of the multiverse. It is interesting and perhaps no coincidence that the best way to understand physics is to focus attention on the underlying principles of symmetry, invariance and equivalence. - David --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.797 / Virus Database: 541 - Release Date: 11/15/2004
Copenhagen Interpretation
This group tends to relate concepts back to MWI. Perhaps CI is a useful way to think as well... At a given point in time, a thinking entity is only aware of a small subset of its surroundings. This suggests an ensemble of all mathematical possibilities that are consistent with that mind in that current state of awareness. This sounds like CI which uses the concept of superposition of states *before* an experiment is performed. - David --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.797 / Virus Database: 541 - Release Date: 11/15/2004
RE: Is the universe computable
Yes, I agree that my definition (although well defined) doesn't have a useful interpretation given your example of perfect squares interleaved with the non perfect-squares. - David -Original Message- From: Kory Heath [mailto:[EMAIL PROTECTED] Sent: Wednesday, 21 January 2004 8:30 PM To: [EMAIL PROTECTED] Subject: RE: Is the universe computable At 1/21/04, David Barrett-Lennard wrote: Saying that the probability that a given integer is even is 0.5 seems intuitively to me and can be made precise (see my last post). We can say with precision that a certain sequence of rational numbers (generated by looking at larger and larger finite sets of integers from 0 - n) converges to 0.5. What we can't say with precision is that this result means that the probability that a given integer is even is 0.5. I don't think it's even coherent to talk about the probability of a given integer. What could that mean? Pick a random integer between 0 and infinity? As Jesse recently pointed out, it's not clear that this idea is even coherent. For me, there *is* an intuitive reason why the probability that an integer is a perfect square is zero. It simply relates to the fact that the squares become ever more sparse, and in the limit they become so sparse that the chance of finding a perfect square approaches zero. Once again, I fully agree that, given the natural ordering of the integers, the perfect squares become ever more sparse. What isn't clear to me is that this sparseness has any affect on the probability that a given integer is a perfect square. Your conclusion implies: Pick a random integer between 0 and infinity. The probability that it's a perfect square is zero. That seems flatly paradoxical to me. If the probability of choosing 25 is zero, then surely the probability of choosing 24, or any other specified integer, is also zero. A more intuitive answer would be that the probability of choosing any pre-specified integer is infinitesimal (also a notoriously knotty concept), but that's not the result your method is providing. Your method is saying that the chances of choosing *any* perfect square is exactly zero. Maybe there are other possible diagnoses for this problem, but my diagnosis is that there's something wrong with the idea of picking a random integer from the set of all possible integers. Here's another angle on it. Consider the following sequence of integers: 0, 1, 2, 4, 3, 9, 5, 16, 6, 25 ... Here we have the perfect squares interleaved with the non perfect-squares. In the limit, this represents the exact same set of integers that we've been talking about all along - every integer appears once and only once in this sequence. Yet, following your logic, we can prove that the probability that a given integer from this set is a perfect square is 0.5. Can't we? -- Kory
RE: Are conscious beings always fallible?
Even if we utilize a language with reflection capability, do we still have an underlying problem with different levels of mathematical truth as indicated by the question of whether 3+4 equals 7? When an expression contains a sub-expression, don't we expect to be able to replace that sub-expression by an equivalent one? But deciding whether two expressions are equivalent depends on a particular perspective of mathematical truth. Btw I thought Smalltalk was weakly typed (can throw a message at any object regardless of type) - David -Original Message- From: Bruno Marchal [mailto:[EMAIL PROTECTED] Sent: Tuesday, 20 January 2004 6:44 PM To: [EMAIL PROTECTED] Subject: Re: Are conscious beings always fallible? I agree with you. Actually you can use the second recursion theorem of Kleene to collapse all the orders. This is easier in an untyped programming language like (pure) LISP than in a typed language, although some typed language have a primitive for handling untyped self-reference, like the primitive SELF in Smalltalk ... Bruno At 23:29 19/01/04 -0800, Eric Hawthorne wrote: How would they ever know that I wonder? Well let's see. I'm conscious and I'm not fallible. Therefore ;-) David Barrett-Lennard wrote: I'm wondering whether the following demonstrates that a computer that can only generate thoughts which are sentences derivable from some underlying axioms (and therefore can only generate true thoughts) is unable to think. This is based on the fact that a formal system can't understand sentences written down within that formal system (forgive me if I've worded this badly). Somehow we would need to support free parameters within quoted expressions. Eg to specify the rule It is a good idea to simplify x+0 to x It is not clear that language reflection can be supported in a completely general way. If it can, does this eliminate the need for a meta- language? How does this relate to the claim above? - David I don't see the problem with representing logical meta-language, and meta-metalanguage... etc if necessary in a computer. It's a bit tricky to get the semantics to work out correctly, I think, but there's nothing extra-computational about doing higher-order theorem proving. http://www.cl.cam.ac.uk/Research/HVG/HOL/ This is an example of an interactive (i.e. partly human-steered) higher-order thereom prover. I think with enough work someone could get one of these kind of systems doing some useful higher-order logic reasoning on its own, for certain kinds of problem domains anyway. Eric
RE: Is the universe computable
Kory said... At 1/21/04, David Barrett-Lennard wrote: This allows us to say the probability that an integer is even is 0.5, or the probability that an integer is a perfect square is 0. But can't you use this same logic to show that the cardinality of the even integers is half that of the cardinality of the total set of integers? Or to show that there are twice as many odd integers as there are integers evenly divisible by four? In other words, how can we talk about probability without implicitly talking about the cardinality of a subset relative to the cardinality of one of its supersets? Saying that the probability that a given integer is even is 0.5 seems intuitively to me and can be made precise (see my last post). Clearly there is a weak relationship between cardinality and probability measures. Why does that matter? Why do you assume infinity / infinity = 1 , when the two infinities have the same cardinality? Division is only well defined on finite numbers. I'm not denying that your procedure works, in the sense of actually generating some number that a sequence of probabilities converges to. The question is, what does this number actually mean? I'm suspicious of the idea that the resulting number actually represents the probability we're looking for. Indeed, what possible sense can it make to say that the probability that an integer is a perfect square is *zero*? -- Kory For me, there *is* an intuitive reason why the probability that an integer is a perfect square is zero. It simply relates to the fact that the squares become ever more sparse, and in the limit they become so sparse that the chance of finding a perfect square approaches zero. - David
RE: Is the universe computable?
Eugen said... I was using a specific natural number (a 512 bit integer) as an example for creation and destruction of a specific integer (an instance of a class of integers). No more, no less. That's plenty to bring out our difference of opinion. cf creation and destruction of a specific integer Existence of a specific integer has nothing to do with existence of a production system for a class of integers. The recipe for a series is not the dish itself. That recipe is also just information, requiring encoding in a material carrier. It would have taken considerably more work to eradicate the entire production system, as it is a bit more widespread, and has a lot more vested interest than conservation of a specific, random integer, destilled from turbulent gas flow. You say a class of integers. Does this mean you don't believe the integers are unique? I guess this is consistent with a non-platonist. However, from the Peano axioms it can be shown that the integers are unique up to isomorphism. Does the concept of uniqueness up to isomorphism seem useful or important to you? The representation (hex, need to be told that above hex string represents an integer (ignoring underlying representations as two's complements, potentials, charge buckets and magnetic domains for the moment) indicates that even that simple information transfer was encrusted with lots of implicit context people take for granted. Roll back to Sumer, and hand out little clay tablets with that hex string. What does it mean? Nothing. Not even the alphabet to parse this exists. Animals evolve representations for quantities, because resource management is a critical survival skill. After a few iterations you get consensual encodings for interactive transfer, then noninteractive consensual encodings. I used patterns of luminous pixels (translated into Braille dots, for all what I know) instead of scratches on a bone fragent, because that encoding is more familiar, and easier to transmit. Wavefront reemitted from pebbles hitting retina, being processed on the fly, tranformed into a spatiotemporal electrochemical activity pattern is an instance of a measurement of a property. It takes a specific class of detectors to do. You cannot conduct that measurement in their absence. The platonist interpretation of the above is simply that context is needed to relate a given sentence (of symbols) back to the Platonic realm. Note that the Platonic realm is *not* itself merely a bunch of sentences. It comes with semantics! You say the given integer exists because it is it is physically realizable *in principle*. That sounds like the platonic view to me - To me, this sounds like a confusion between a specific integer, and a recipe for such. It is quite difficult to feed a wedding throng with pages from a cookbook. I can't work out what you are saying! You use terms like specific integer and I've got no idea what you mean because you don't believe concepts exist independently of their production systems. The integers are an example of a concept that is *decoupled* from specific instances - by definition. A great deal of our thinking and language involves generalisation. For example the word chair is associated with a class of objects. You use generalisation in your sentences as much as anyone else. Your lines of reasoning treat these abstractions as things that can be manipulated - such as when I say the boy kicked the ball and you form an image in your mind - even though the sentence involves generalisations such as boy and ball. I presume your refutation (as a non-platonist) is that concepts only exist while someone (or something) is there to think them. The problem with that view is that many useful lines of reasoning involve the question Does there exist a concept x such that p(x) without instantiating x. In other words, it seems to be useful to conceptualise over the space of all possible concepts. This is exactly what happens when we generalise specific integers to the infinite set of all integers. I don't see how the non-platonist can accept any lines of reasoning that involve the set of integers because it is impossible to conceptualise every member of the set which (to them) would imply that the set doesn't exist. You agreed before with the hypothesis that a computer could exhibit awareness. Suppose we have (say on optical disk) a program and we have a computer on which we can run the program, but we haven't run the program yet. We can a-priori ask the question On the computer monitor, will we see a simulated person laugh?. Do you believe this a-priori question has an a-priori answer? After all, there is nothing mystical in a deterministic computation. If so doesn't that mean that the simulated person exists independently of running the actual simulation? In fact, if we postulate that our universe is computable, then the question Does there exist a person who laughs on
RE: Is the universe computable?
Hi Eric, 0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780 didn't exist in this universe (with a very high probability, it being a 512 bit number, generated from physical system noise) before I've generated it. Now it exists (currently, as a hex string (not necessarily ASCII) on many systems (...) You admit a base 16 notation for numbers - which means you allow numbers to be written down that aren't physically realized by the corresponding number of pebbles etc. So much for talking about pebbles in your previous emails! I think that it doesn't matter what base you choose to write down the number. It is an integer, therefore it is physically realizable *in principle*. If you write '1aa3' in base 16, it means '6893' in base 10, which corresponds to a given number of pebbles. We may think that there is somehow more reality in 6893 in comparison to 1aa3, but they are both in the same footing, except that we are more used to the first representation. Why would one claim that the corresponding decimal representation of Eugen's 512-bit number has any more reality that the hexadecimal one? I agree with everything you say, but did you really think I was making a point because Eugen happened to use hex?! You say the given integer exists because it is it is physically realizable *in principle*. That sounds like the platonic view to me - because the number is *not* actually physically realized and yet the number is purported to have an independent existence. Are you saying otherwise? I think any form of symbolic manipulation of numbers is implicitly using the platonic view. To say they spring into existence as they are written down (which in any case only means they are realizable in principle) just seems silly to me. I have no formed opinion on arithmetical realism, even though I tend to accept that there is some external reality to the integers. But is the reality that is assigned to numbers of the same kind that is assigned to their physical representation? Are we not discussing just words without any meaning? The Platonic view just says that every mathematical system free from contradiction exists. Ie if it can exist then it does exist. There is no need to talk about different types of reality. - David
Re:Is the universe computable?
Hi Eugen, Yeah. I'm saying that, say, 0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780c2ccdf0c8e100d38f20 d9 f3064aea3fba00e723a5c7392fba0ac0c538a2c43706fdb7f7e58259 didn't exist in this universe (with a very high probability, it being a 512 bit number, generated from physical system noise) before I've generated it. Now it exists (currently, as a hex string (not necessarily ASCII) on many systems around the world, rendered in diverse fonts), as soon as I remove all its encodings it's gone again. P00f! I can't identity with your conception of numbers but I guess you're entitled to it! You admit a base 16 notation for numbers - which means you allow numbers to be written down that aren't physically realized by the corresponding number of pebbles etc. So much for talking about pebbles in your previous emails! In statements of the form There exists integer x such that p(x) do you say this is vacuous because x hasn't been specified yet, or is it sufficient to merely name an unspecified integer to allow it to exist? Many proofs make these sorts of statements, and no where is the named integer given a specific value (even though its purported existence is crucial to the proof). Do you say these proofs are vacuous? If I write the statement for all integer x, x+1 x, does this make all the integers come into existence? Or is this another vacuous statement? - David
RE: Is the universe computable?
Hi Eugin, I see, we're at the prove that the Moon is not made from green cheese when nobody is looking stage. I thought this list wasn't about ghosties'n'goblins. Allright, I seem to have been mistaken about that. You seem to be getting a little hot under the collar! Here is a justification of why I think arithmetical realism is at least very plausible... Let's suppose that a computer simulation can (in principle) exhibit awareness. I don't know whether you dispute this hypothesis, but let's assume it and see where it leads. Let's suppose in fact that you Eugin, were able to watch a computer simulation run, and on the screen you could see people laughing, talking - perhaps even discussing ideas like whether *their* physical existence needs to be postulated, or else they are merely part of a platonic multiverse. A simulated person may stamp his fist on a simulated coffee table and say Surely this coffee table is real - how could it possibly be numbers - I've never heard of anything so ludicrous!. Now Eugin, you may argue that the existence of this universe depends on the fact that it was simulated by a computer in our universe. I find this a little hard to fathom - because computer simulations are deterministic and they give the same results whether they are run once or a thousand times. I find it hard to imagine that they leap into existence when they are run the first time. I'm particularly motivated by the universal dove-tailing program - which eventually generates the trace of all possible programs. Do you say that most of the integers don't exist because nobody has written them down? I can see your point when you say that 2+2=4 is meaningless without the physical objects to which it relates. However this is irrelevant because you are thinking of too simplistic a mathematical system! The only mathematical systems that are relevant to the everything-list are those that have conscious inhabitants within them. Within this self contained mathematical world we *do* have the context for numbers. It's a bit like the chicken and egg problem. (egg = number theory, chicken = objects and observers). Both come together and can't be pulled apart. - David -Original Message- From: Eugen Leitl [mailto:[EMAIL PROTECTED] Sent: Wednesday, 14 January 2004 1:32 AM To: [EMAIL PROTECTED] Subject: Re: Is the universe computable? On Tue, Jan 13, 2004 at 03:03:38PM +0100, Bruno Marchal wrote: What is the point? Do we have experimental procedure to validate the opposite of the fanciful scenario? Giving that we were talking about I see, we're at the prove that the Moon is not made from green cheese when nobody is looking stage. I thought this list wasn't about ghosties'n'goblins. Allright, I seem to have been mistaken about that. first person scenario, in any case it is senseless to ask for experimental procedure. (experience = first person view; experiment = third person view). So the multiverse is not a falsifyable theory? Don't tell me you were believing I was arguing. You were asserting a lot of stuff. That's commonly considered arguing, except you weren't providing any evidence so far. So, maybe you weren't. About logic, it is a branch of mathematics. Like topology, algebra, analysis it can be *applied* to some problem, which, through some hypothesis, can bear on some problem. With the comp hyp mathematical logic makes it possible to derive what consistent and platonist machine can prove about themselves and their consistent extension. Except that machine doesn't exist in absence of implementations, be it people, machines, or aliens. My point is that formal systems are a very powerful tool with very small reach, unfortunately. But I never use formal system. I modelise a particular sort of machine by formal system, so I prove things *about* machines, by using works *about* formal system. I don't use formal systems. I prove things in informal ways like all mathematicians. Above passage is 100% content-free. Because we know that QM is not a TOE. You haven't heard? How could be *know* QM is not a TOE? (I ask this independently of the fact that I find plausible QM is not a *primitive* TOE). Because general relativity and quantum theory are mutually incompatible. So both TOE aren't. We have several TOE candidates, and an increased number of blips heralding new physics, but no heir apparent yet. You believe that the theorem there is an infinity of primes is a human invention? (as opposed to a human discovery). Of course. Not necessarily human; there might be other production systems which invented them. Then, maybe there aren't. Infinity is something unphysical, btw. You can't represent arbitrary values within a finite physical system -- all infoprocessing systems are that. You'll also notice that imperfect theories are riddled with infinities; they tend to go away with
RE: Peculiarities of our universe
Let X be some predicate condition on the universes in the multiverse. I think Hal is assuming that if all the following are true 1. X can be described in a compact form (ie it doesn't fill up a book with detailed data) 2. X is true for our universe 3. AUH = P(X)=0 then we deduce that AUH is (probably) false. Are you saying Wei, that there is a flaw in this logic? - David -Original Message- From: Wei Dai [mailto:[EMAIL PROTECTED] Sent: Tuesday, 13 January 2004 9:22 AM To: Hal Finney Cc: [EMAIL PROTECTED] Subject: Re: Peculiarities of our universe On Sun, Jan 11, 2004 at 09:57:18AM -0800, Hal Finney wrote: [...] That is (turning to the Schmidhuber interpretation) it must be much simpler to write a program that just barely allows for the possibility of life than to write one which makes it easy. This is a prediction of the AUH, and evidence against it would be evidence against the AUH. evidence against it would be evidence against the AUH is similar to the Doomsday Argument. Let's assume that in fact universes with lots of intelligent life don't all have much lower measure than our own. Then AUH implies the typical observer should see many nearby intelligent life. Your argument is that since we don't see many nearby intelligent life, AUH is probably false. In the Doomsday Argument, the non-doomsday hypothesis implies the typical observer should have a high birth rank, and the argument is that since we have a low birth rank, the non-doomsday hypothesis is probably false. I want to point this out because many people do not think the DA is valid and some have produced counterarguments. Some of those counterarugments may work against Hal's argument as well.
RE: Is the universe computable?
Georges Quenot wrote: Also I feel some confusion between the questions Is the universe computable ? and Is the universe actually 'being' computed ?. What links do the participants see between them ? An important tool in mathematics is the idea of an isomorphism between two sets, which allows us to say *the* integers or *the* Mandelbrot set. This allows us to say *the* computation, and the device (if any) on which it is run is irrelevant to the existence of the computation. This relates to the idea of the Platonic existence of mathematical objects. This makes the confusion between the above questions irrelevant. I think it was John Searle (who argues that computers can't be aware) who said A simulation of a hurricane is not a hurricane, therefore a simulation of mind is not mind. His argument breaks down if *everything* is a computation - because we can define an isomorphism between a computation and the simulation of that computation. - David
RE: Is the universe computable?
Jesse Mazer wrote, Isn't there a fundamental problem deciding what it means for a given simulated object to implement some other computation? Yes, but does this problem need to be solved? I have no problem with the idea that some physical object (in one computation) can be interpreted in all sorts of ways - depending on how you map it. Does it matter if there exists a (weird) mapping between a rock and a universe with conscious inhabitants? The universe doesn't depend on the rock for its existence so who cares! - David
RE: Bio of Hugh Everett, III is posted
Hi Bruno, How successful would you say has been the idea to derive QM from number theory? What proportion of physicists are aware of this idea? How does it relate to the Russell Standish derivation of QM? David -Original Message- From: Bruno Marchal [mailto:[EMAIL PROTECTED] Sent: Tuesday, 23 December 2003 7:28 PM To: [EMAIL PROTECTED] Subject: Re: Bio of Hugh Everett, III is posted Indeed. Another illuminating passage is that Everett *did* compare the observer with an amoeba with a good memory, and thus did relate the QM subjective indeterminacy with the comp first person indeterminacy, ... and then Wheeler asked him to suppress that passage!!! That makes it still a bigger mystery for me that Everett did not see the simpler comp immortality, and the necessity to derive QM from number theory ..., and this despite Everett's interest in computer science, as the paper also illustrates well. Bruno
RE: Why is there something rather than nothing?
Jesse said So, although the set of all well-defined finite descriptions must clearly be countable in the traditional sense where arbitrary mappings are allowed, it is not countable if only finite-describable mappings are allowed, although it can easily be shown to be smaller than another countable set, namely the set of all finite descriptions without regard for whether they are well-defined or not Doesn't this unintuitive result show that you are doomed if you only believe in the platonic existence of mathematical objects with finite descriptions? Was this the point you were making, despite saying earlier you were skeptical of the existence of objects without a finite description? - David
Move versus assign
We observe that our universe uses a reversible computation, yet our brains only appear to use irreversible computation. It seems important to ask why. Is it possible for SASs to live in a universe that is directly associated with an irreversible computation? If so then why are we special? Computer science seems to be centered around the concept of assignment. For example, computer memory undergoes state changes in the form of assignments to memory locations. A Turing machine uses assignment operations each time a 1 or 0 is written on the tape. Assignment involves lost information because it simply overwrites the previous value with a new value. It is fundamentally irreversible. I have been wondering whether we can get a better understanding of reversible computation by distinguishing between movement of information and assignment of information. The analogy of the Turing machine would be that we need to cut up the tape with scissors we are only allowed to move bits of tape around, rather than reassign values on the tape. This leads quickly to the view of particles that move around, rather than the idea of a particle that is stored in space (= memory) that moves as the result of assignments to space. So rather than think of a small piece of space having an attribute of what particle is in it, we should think of a particle as having an attribute of where it is in space. The latter view makes space seem rather incidental rather than thinking of particles as being embedded in space. I wonder to what extent physicists distinguish between these two views. I guess the distinction evaporates in string theory, where there is nothing but (higher dimensional) space-time. There is nothing to assign to because the information is present in the topology of space itself. Movement of information is more like a ripple on a pond. The Turing machine seems to lack a direct relevance to our universe. However, cant a Turing machine emulate a reversible computation? - David
RE: Move versus assign
Russell said... In answer to the original question, I would conjecture that an evolutionary process is the only process capable of generating complexity. Since we need a certain amount of complexity to be conscious, it follows that the simplest universes are ensembles of possibilities, on which anthropic selection acts to generate the needed complexity. Ensemble universes can only evolve by reversible processes - otherwise possibilities are irretrievably lost over time. Do you think in terms of an ensemble of Turing machines, of which only a few emulate reversible processes? So do we have an irreversible computation on a Turing machine emulating a reversible computation for the universe emulating a brain doing an irreversible computation? - David
RE: Move versus assign
Hi Stephen, The thermodynamic arrow of time only seems to be related to the boundary conditions of the universe, rather than those laws of physics which we regard as independent from the boundary conditions. The success of being able to divide and conquer physics into bc laws / non bc laws is interesting and remarkable. - David -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED] Sent: Monday, 24 November 2003 11:55 AM To: [EMAIL PROTECTED] Subject: Re: Move versus assign Dear David, Please explain the claim : We observe that our universe uses a reversible computation. I do not see how this follows from the observation that, on every observable scale, there is a non-invertible (thermodynamic) arrow of time. I do not see how this is possible if your claim holds. We can add to this the strong evidence that our universe is open and very close to being flat. Kindest regards, Stephen - Original Message - From: David Barrett-Lennard To: [EMAIL PROTECTED] Sent: Sunday, November 23, 2003 9:14 PM Subject: Move versus assign We observe that our universe uses a reversible computation, yet our brains only appear to use irreversible computation. It seems important to ask why. Is it possible for SASs to live in a universe that is directly associated with an irreversible computation? If so then why are we special? Computer science seems to be centered around the concept of assignment. For example, computer memory undergoes state changes in the form of assignments to memory locations. A Turing machine uses assignment operations each time a 1 or 0 is written on the tape. Assignment involves lost information because it simply overwrites the previous value with a new value. It is fundamentally irreversible. I have been wondering whether we can get a better understanding of reversible computation by distinguishing between movement of information and assignment of information. The analogy of the Turing machine would be that we need to cut up the tape with scissors we are only allowed to move bits of tape around, rather than reassign values on the tape. This leads quickly to the view of particles that move around, rather than the idea of a particle that is stored in space (= memory) that moves as the result of assignments to space. So rather than think of a small piece of space having an attribute of what particle is in it, we should think of a particle as having an attribute of where it is in space. The latter view makes space seem rather incidental rather than thinking of particles as being embedded in space. I wonder to what extent physicists distinguish between these two views. I guess the distinction evaporates in string theory, where there is nothing but (higher dimensional) space-time. There is nothing to assign to because the information is present in the topology of space itself. Movement of information is more like a ripple on a pond. The Turing machine seems to lack a direct relevance to our universe. However, cant a Turing machine emulate a reversible computation? - David
RE: Why is there something rather than nothing?
Therefore the reals would have to include all kinds of numbers that
have
no
finite description at all. I am not sure I believe such things exist,
and
for a similar reason I am not sure I believe that every member of the
hypothetical power set of the integers exists either.
Hi Jesse,
I think you are asking an important question. I think it relates to
self referencing definitions - which is implicit in the axiomatic
approach.
Here's a go at defining the describable reals...
The formal axiom that distinguishes the reals from the rationals is the
completeness axiom. This can take a number of different forms. One
version is : Every set bounded above has a supremum.
Let Q be the set of rationals. This is a solid starting point because
every rational has a finite description.
Consider that we restrict ourselves to sets of the form
X = { x in Q | p(x) }
where p(x) is a predicate on a rational number x. Given that every
rational has a finite description, and p(x) is associated with a finite
description, we deduce that X and all its members are describable.
The completeness axiom says that X has upper bound = sup(X) exists.
It seems to me that we can take this as a way of defining the
*describable* reals like sqrt(2) or pi - because it is precisely the
holes in the set of rationals that make us want to plug them up.
Eg sqrt(2) = sup { x in Q | x^2 2 }
Naturally, we will only be able to describe countably many numbers in
this way. Let's call this set R.
Note that R was defined in terms of completing the rationals, rather
than completing itself which is the normal axiomatic way of defining
the reals.
A self reference approach would have been to write
X = { x in R | p(x) }
So that we are using the reals to define the reals!
- David
RE: Why is there something instead of nothing?
The set of everything U is ill defined.
Given set A, we expect to be able to define the subset { x is element of
A | p(x) } where p(x) is some predicate on x.
Therefore given U, we expect to be able to write S = { x an element of U
| x is not an element of x }
Now ask whether S is an element of S.
- David
-Original Message-
From: George Levy [mailto:[EMAIL PROTECTED]
Sent: Monday, 17 November 2003 2:15 PM
To: [EMAIL PROTECTED]
Subject: Re: Why is there something instead of nothing?
John Collins wrote:
One interpretation of
the universe of constructible sets found in standard set theory
textbooks
is
that even if you start with nothing, you can say that's a thing,
and
put
brackets around it and then you've got two things: nothing and
{nothing}.
And then you also have {nothing and {nothing}}
Why start with nothing? Isn't this arbitrary?
In fact zero information = all possibilities and all information = 0
possibility.
of course, (0 possibility) = 1 possibililty
What is not arbitrary? Certainly anything is arbitrary. The least
arbitrary seems to be everything which is in fact zero information.
.
Start with the set(everything) and start deriving your numbers.
To do this, instead of using the operation set( ), use the operation
elementof( ).
Hence one=elementof(everything) and two = elementof(everything - one);
three = elementof(everything - one - two)
George
RE: spooky action at a distance
I'm sure we all agree that QM on its own is not the full story. Ditto with GR. Has anyone claimed to come up with a self consistent, complete description of our universe? Saying that all universes exist which follow the MWI is putting too much faith in a partial (and perhaps merely approximate) model of our universe. With your line of reasoning you would say that people's consciousness differentiated at the time QM displaced classical physics. Surely QM was waiting to be discovered? For this reason, I think it is important that we look for better ontologies of QM. Even though these different interpretations make the same predictions today, they affect the way we reason about things - and our ability to extend the model in new directions. Anton Zeilinger has brought up the example of Einstein's publication of special relativity which provided the missing ontology - when most of the equations had already been provided by Lorentz, Fitzgerald etc. There is no doubt that this ontology had enormous benefit. - David -Original Message- From: Hal Finney [mailto:[EMAIL PROTECTED] Sent: Friday, 14 November 2003 1:31 AM To: [EMAIL PROTECTED] Subject: Re: spooky action at a distance This list is dedicated to exploring the implications of the prospect that all universes exist. According to this principle, universes exist with all possible laws of physics. It follows that universes exist which follow the MWI; and universes exist where only one branch is real and where the other branches are eliminated. Universes exist where the transactional interpretation is true, and where Penrose's objective reduction happens. I'm tempted to even say that universes exist where the Copenhagen interpretation is true, but that seems to be more a refusal to ask questions than a genuine interpretation. Therefore it is somewhat pointless to argue about whether we are in one or another of these universes. In fact, I would claim that we are in all of these, at least all that are not logically inconsistent or incompatible with the data. That is, our conscious experience spans multiple universes; we are instantiated equally and equivalently in universes which have different laws of physics, but where the differences are so subtle that they have no effect on our observations. It may be that at some future time, we can perform an experiment which will provide evidence to eliminate or confirm some of these possible QM interpretations. At that time, our consciousness will differentiate, and we will go on in each of the separate universes, with separate consciousness. It is still useful to discuss whether the various interpretations work at all, and whether they are in fact compatible with our experimental results. But to go beyond that and to try to determine which one is true is, according to the multiverse philosophy, an empty exercise. All are true; all are instantiated in the multiverse, and we live in all of them. Hal
RE: spooky action at a distance
By small I meant small number of particles. - David -Original Message- From: scerir [mailto:[EMAIL PROTECTED] Sent: Thursday, 13 November 2003 6:06 PM To: [EMAIL PROTECTED] Subject: Re: spooky action at a distance David Barrett-Lennard According to QM, in small systems evolving according to the Hamiltonian, time certainly exists but there is no arrow of time within the scope of the experiment. In such small systems we can run the movie backwards and everything looks normal. Yes, but how small? Because now they perform experiments over large distance. Not just the 45 meters of the old Jasin interferometer. But 10 km. or even 100 km. And still they find interferences. (Of course those beams are correlated and well protected!). In general the argument 'contra' the transactional interpretation is this one below (in this case, by Anton Zeilinger). But I do not know well enough Cramer's interpretation. So I cannot judge. In the Transactional Interpretation the state vector is considered to be a real physical wave emitted as an offer wave based on the preparation procedure of the experiment. The interaction then comes to a close through the emission of the confirmation wave by what is usually called the collapse of the wave function. The quantum particle, e.g. the photon, electron etc., is then considered to be identical with the finished transaction. It is fundamental to that interpretation that where the closure of the transaction takes place is an unexplained input to the process.
RE: Last-minute vs. anticipatory quantum immortality
I might still occasionally face accidents where I had to be very lucky to survive, but the lower the probability there is of surviving a particular type of accident, the less likely I am to experience events leading up to such an accident. So if someone is on a cliff about to commit suicide, from his perspective, he will probably find he can't go through with it? In fact will a suicidal person find that nothing tends to go wrong in his life (because if it did he would want to commit suicide)? The more suicidal he is the better! Or perhaps there is a vanishingly small probability of finding yourself so easily depressed even though it is not unreasonable to come across other people that are. But if the tendency to be suicidal is inherited in the genes can it be that this is anticipatory as well? Of course at the time you inherit your genes you aren't conscious. - David -Original Message- From: Jesse Mazer [mailto:[EMAIL PROTECTED] Sent: Wednesday, 12 November 2003 5:34 PM To: [EMAIL PROTECTED] Subject: Last-minute vs. anticipatory quantum immortality From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: Re: Fw: Quantum accident survivor Date: Sat, 08 Nov 2003 15:56:31 +0100 At 14:36 07/11/03 -0800, Hal Finney wrote: snip Well, I do believe in continuity of consciousness, modulo the issues of measure. That is, I think some continuations would be more likely to be experienced than others. For example, if you started up 9 computers each running one copy of me (all running the same program so they stay in sync), and one computer running a different copy of me, my current theory is that I would expect to experience the first version with 90% probability. Almost OK, but perhaps false if you put *the measure* on the (infinite) computations going through those states. I mean, if the 9 computers running one copy of you just stop (in some absolute way I ask you to conceive for the benefit of the argument), and if the one computer running the different copy, instead of stopping, is multiplied eventually into many self-distinguishable copies of you, then putting the measure on the histories should make you expect to experience (and memorized) the second version more probably. It is the idea I like to summarize in the following diagram: \/ | | \/ | | \/ =| | | | | | | | That is, it is like a future bifurcation enhances your present measure. It is why I think comp confirms Deutsch idea that QM branching is really QM differentiation. What do you think? I mean, do you conceive that the measure could be put only on the maximal possible computations? Bruno This is an important point which I think people often miss about the QTI. It is sometimes spoken of as if the QTI only goes into effect at the moment you are about to die (and thus have no successor observer-moment), which would often require some fantastically improbable escape, like quantum tunneling away from a nearby nuclear explosion. But if later bifurcations can effect the first-person probability of earlier ones, this need not be the case. Consider this thought experiment. Two presidential candidates, let's say Wesley Clark and George W. Bush, are going to be running against each other in the presidential election. Two months before the election, I step into a machine that destructively scans me and recreates two copies in different locations--one copy will appear in a room with a portrait of George W. on the wall, the other copy will appear in a room with a portrait of Wesley Clark. The usual interpretation of first-person probabilities is that, all other things being equal, as the scanner begins to activate I should expect a 50% chance that the next thing I see will be the portrait of George W. appearing before me, and a 50% chance that it will be Wesley Clark. But suppose all other things are *not* equal--an additional part of the plan, which I have agreed to, is that following the election, the copy who appeared in the room with the winning candidate will be duplicated 999 times, while the copy who appeared in the room with the losing candidate will not experience any further duplications. Thus, at any time after the election, 999 out of 1000 versions of me who are descended from the original who first stepped into the duplication machine two months before the election will remember appearing in the room with the candidate who ended up winning, while only 1 out of 1000 will remember appearing in the room with the losing candidate. The last minute theory of quantum immortality is based on the idea that first-person probabilities are based solely on the observer-moments that qualify as immediate successors to my current observer-moment, and this idea suggests that as I step into the duplication machine two months
Reversible computing
I have been wondering whether there is something significant in the fact that our laws of physics are mostly time symmetric, and we have a law of conservation of mass/energy. Does this suggest that our universe is associated with a reversible (and information preserving) computation? - David
RE: Reversible computing
Assuming neurons aren't able to tap into QM stuff because of decoherence, it seems odd that consciousness is performed with an irreversible computation whilst the universe uses a reversible computation. - David -Original Message- From: Russell Standish [mailto:[EMAIL PROTECTED] Sent: Thursday, 13 November 2003 9:59 AM To: David Barrett-Lennard Subject: Re: Reversible computing I think the answer to your question is yes (assuming I understand you correctly). Information and probability are closely linked (through algorithmic information theory - AIT for those acronym lists). Schroedinger's equation is known to conserve probability (basically |\psi(t)| is a constant - usually set to 1 - under evolution by Schroedinger's equation (|.| here means Hilbert spoace norm, not absolute value)). This conservation of probability turns out to be equivalent to unitarity of the Hamiltonian operator, which guess what, means energy is conserved. Unitary evolution is a reversible computation, which is why quantum computations are reversible. Cheers David Barrett-Lennard wrote: I have been wondering whether there is something significant in the fact that our laws of physics are mostly time symmetric, and we have a law of conservation of mass/energy. Does this suggest that our universe is associated with a reversible (and information preserving) computation? - David A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02
RE: Reversible computing
I havent read much about invertible systems. Curiously though, earlier this year I was working on a difficult problem related to optimistic concurrency control in a distributed object oriented database Im developing, and found that I only solved it when I decomposed it as an invertible problem into parts that were invertible. The decomposition always involved invertible functions with two inputs and two outputs. All state changes (to a local database) are applied as invertible operations, and the problem is to transform operations so they can be applied in different orders at different sites and yet achieve convergence. I guess its unlikely that this has relevance to physics. - David -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED] Sent: Thursday, 13 November 2003 10:14 AM To: [EMAIL PROTECTED] Subject: Re: Reversible computing Dear David, Have you read any of the books by Michael C. Mackey on the implications of reversible (invertible) and non-invertible systems? Some, notably Oliver Penrose, have attacked his reasoning, but I find his work to be both insightful and novel and that his detractors are mostly driven by their own inabilities to take statistical dynamics and thermodynamics forward. Mackey shows that invertible dynamical system will be at equilibrium perpetually and that only non-invertible system will exhibit an arrow of time. I am very interested in the subject of reversible computation, as it relates to my study of Hitoshi Kitada's theory of Time, and would like to learn about what you have found about them. Kindest regards, Stephen - Original Message - From: David Barrett-Lennard To: [EMAIL PROTECTED] Sent: Wednesday, November 12, 2003 8:36 PM Subject: Reversible computing I have been wondering whether there is something significant in the fact that our laws of physics are mostly time symmetric, and we have a law of conservation of mass/energy. Does this suggest that our universe is associated with a reversible (and information preserving) computation? - David
RE: Quantum accident survivor
I'm trying to define identity... Let's write x~y if SAS's x and y (possibly in different universes) have the same identity. I propose that this relation must be reflexive, symmetric and transitive. This neatly partitions all SAS's into equivalence classes, and we have no ambiguity working out whether any two SAS's across the multi-verse have the same identity. Consider an SAS x that splits into x1, x2 (in child universes under MWI). We assume x~x1 and x~x2. By symmetry and transitivity we deduce x1~x2. So this definition of identity is maintained across independent child universes. This is at odds with the following concept of identity... I am, for all practical purposes, one and only one specific configuration of atoms in a specific universe. I could never say that ' I ' is ALL the copies, since I NEVER experience what the other copies experience It seems necessary to distinguish between a definition of identity and the set of memories within an SAS at a given moment. Is it possible that over long periods of time, the environment can affect an SAS to such an extent that SAS's in different universe that are suppose to have the same identity actually have very little in common? What happens if we splice two SAS's (including their memories)? It seems to me that the concept of identity is not fundamental to physics. It's useful for classification purposes as long as one doesn't stretch it too far and expose its lack of precision. This reminds me of the problem of defining the word species. Although a useful concept for zoologists it is not well defined. For example there are cases where (animals in region) A can mate with B, B can mate with C, but A can't mate with C. - David
RE: Quantum accident survivor
Yes this helps, but I still find it strange to talk about offspring universes (that by definition are independent) and yet to predict outcomes we sum their complex valued wave functions. While we're on the subject of interpretation of QM, do you know about the transactional interpretation of QM? I find this more natural than Copenhagen or MWI - particularly with its explanation of spooky action at a distance. I particularly like the explanation of inertia (as arising through advanced waves sent backwards in time from the rest of the universe). This is a simple and natural explanation of the equivalence principle in general relativity. It also explains why an inertial frame of reference doesn't rotate with respect to the fixed stars. Given the time symmetry in the laws of physics, we expect small systems of elementary particles won't have an arrow of time - because that is only a feature of macro systems starting in a low entropy state. Therefore waves that travel backwards in time (ie advanced waves) must be a fundamental (inevitable) concept. Doesn't all QM strangeness arise naturally from this? Why not invoke Occam's razor and drop the idea of many worlds? - David -Original Message- From: Matt King [mailto:[EMAIL PROTECTED] Sent: Saturday, 8 November 2003 3:37 AM To: David Barrett-Lennard Cc: [EMAIL PROTECTED] Subject: Re: Quantum accident survivor Hello David, David Barrett-Lennard wrote: Please note that my understanding of QM is rather lame... Doesn't MWI require some interaction between branches in order to explain things like interference patterns in the two slit experiment? What does this mean for the concept of identity? - David There is a technical difference between interference and interaction. Interaction refers to two or more particles influencing each other through the exchange of force. Only particles within the same universe (within the broader multiverse) may interact with each other in this way. These particles are represented by wavefunctions in quantum mechanics, which have wavy properties like amplitude and wavelength, and so can exhibit interference just like waves on a pond. Also just like waves on a pond, particle wavefunctions can pass through each other, even annihilating completely in some places, without interacting (i.e. without exchanging force). Typically in single-particle experiments like Young's double slits, there is no interaction, and the interference arises from the sum of all the different trajectories (or worlds if you like) that the particle may have taken. In experiments involing two or more particles, frequently every possible path of each particle and every possible interaction must be considered as a separate world. Interference then takes place between these possible worlds, and must be taken into account in order to correctly make statistical predictions of how the particle system will behave. So in answer to your question, no, the MWI does not require interaction between branches to explain interference. Indeed interaction (exchange of force) is prohibited by the linearity of the Schroedinger Wave Equation (SWE), which indicates that its different possible solutions (universes) should move through each other as easily as ripples through a pond. We can only see the interference when we're not interacting with the rippling system. Once we do, the rippling system expands to include us within its folds. From that point on, there are multiple versions of us, each experiencing a different ripple, completely unable to interact with the other versions of ourselves moving through us all the time. Hope this helps, Matt. When God plays dice with the Universe, He throws every number at once...
RE: Quantum accident survivor
I have a feeling some of these points of view are not falsifiable (and therefore somewhat meaningless). An individual that is about to experience a QM immortality episode can't perform additional experiments to answer (philosophical) questions about his identity. The only observable is the survivor who can talk about who he is and what he remembers. Please note that my understanding of QM is rather lame... Doesn't MWI require some interaction between branches in order to explain things like interference patterns in the two slit experiment? What does this mean for the concept of identity? - David
RE: Is the universe computable?
An interesting idea. Where can I read a more comprehensive justification of this distribution? If a number of programs are isomorphic the inhabitants naturally won't know the difference. As to whether we call this one program or lots of programs seems to be a question of taste and IMO shows that probability calculations are only relative to how one wants to define equivalence classes of programs. I would expect that the probability distribution will depend on the way in which we choose to express, and enumerate our programs. Eg with one instruction set, infinite loops or early exits may occur often - so that there is a tendency for simplistic programs. On the other hand, an alternative instruction set and enumeration strategy may lead to a distribution favoring much longer and more complex programs. Perhaps it tends to complicate programs with long sequences of conditional assignment instructions to manipulate the program state, without risking early exit. Importantly such tampering doesn't yield a program that is isomorphic to a simple one. We seem to have a vast number of complicated programs that aren't reducible to simpler versions. This seems to be at odds with the premise (of bits that are never executed) behind the Universal Distribution. - David -Original Message- From: Hal Finney [mailto:[EMAIL PROTECTED] Sent: Tuesday, 4 November 2003 2:24 PM To: [EMAIL PROTECTED] Subject: RE: Is the universe computable? IMO the best idea we have discussed for why the universe is and remains lawful is that the set of descriptions (equivalently, programs) for the universes are governed by the Universal Distribution. This is the description where a string whose shortest description has length n bits is given measure 1 / 2^n. An heuristic argument for this distribution is that if programs are self delimiting, then there are 2^x more programs of length n+x than of length n, created by appending the 2^x x-bit strings to each n-bit program. Since the appended x bits are never executed, all 2^(n+x) of these programs are the same as the basic 2^n programs. A program which says obey these simple laws is shorter than a program which says obey these simple laws for a zillion steps, then start obeying these other laws, or a program that says obey these simple laws everywhere except where this incredibly complicated configuration occurs, and then do this complicated other thing. Hal Finney
RE: Is the universe computable?
Russell, My personally preferred solution to this problem is described in my paper Why Occam's Razor. I agree that extra bits in the program would tend to appear as noise rather than some miracle like a fire breathing dragon. Is it then assumed that the magnitude of this noise is unlikely to be seen - even in a delicate physics experiment because tampering is so improbable, or is it in fact measurable, arising in the form of QM uncertainty? - David
