Re: Is the universe computable?
Norman Samish : Max Tegmark, at http://207.70.190.98/toe.pdf, published in Annals of Physics, 270, 1-51 (1998), postulates that all structures that exist mathematically exist also physically. Max Tegmark postulated or conjectured even more in that paper: that the distinction between mathematical existence and physical existence is meaningless, at least from a scientific point of view. I also had this idea about two years ago: if (this is not a small if but this is the assupmtion here) the universe is isomorphic to a mathematical (presumably arithmetic) object, it must be this very object since all isomorphic objects are the same object. In other words (probably inaccurately but ine can grasp the idea anyway): no matter what substance particles are made of as long as they obey a given set of equations/rules, everything that does happen as we perceive it depends only of this given set of equations/rules, and not at all of any hypothetical substance the particles would be made of. If the substance of particle does not matter, it doesn't even matter that they have any substance at all and every question (nature, existence, ...) about such hypothetical substance is purely metaphysical. There are however several assumptions behind this idea, at least the one mentionned above and another one about arithmetical realism. Incidently, I found this mailing list (and soon after Tegmark's paper) by trying to figure how original that idea might be and how seriously it could be taken (I just entered the question Do natural numbers exist by themselves ? or possibly a variant of it like Who supports the idea that natural numbers exist by themselves ? in the general purpose question answering system: http://www.languagecomputer.com/demos/question_answering/internet_demo/index.html). Georges Quénot.
Re: Is the universe computable?
Bruno Marchal wrote: At 11:34 08/01/04 +0100, Georges Quenot wrote: I am very willing (maybe too much, that's part of the problem) to accept a Platonic existence for *the* integers. I am far from sure however that this does not involve a significant amount of faith. Indeed. It needs an infinite act of faith. But I have no problem with that ... Unfortunately, it seems that some people do. I am not sure how much I share that faith. As I mentionned, I am willing to but since I could not find some ground to support that willingness, I might be a bit agnostic too. There are some objections to it and I am not sure that none of them make sense. Also, as someone said (if anybody has the original reference, in am interested): the desire to believe is a reason to doubt. I think that, even if it is true, arithmetic realism needs to be postulated (or conjectured) since I can't figure how it could be established. All right. That's why I explicitly put the AR in the definition of computationalism. About your question is the universe computable? the problem depends on what you mean by universe. The definition you gave recently are based on some first person point of view, and even that answer does not makes things sufficiently less ambiguous to answer. Don't hesitate to try again. I have no problem with definitions that inculde some first person point of view. I do not find them so first person point of view since I believe that every person I can talk with, using the same first person point of view, would see the same universe. We could at least say the universe in a consistent way among us. I might try again but I would like first to see what others have to say on the subject (to get an idea of in what direction I would need to make things clearer). You can also read my thesis which bears on that subject (in french). Yes. I have found the reference too. One of my next readings I think (though I have a pipe quite full...). You may be interested in learning that at least the *physical* universe cannot be computable once we postulate the comp hypothesis (that is mainly the thesis that I or You are computable; + Church thesis + AR). The reason is that with comp, as with Everett (and despite minor errors in Everett on that point), the traditional psycho-parallelism cannot be maintained. See my URL below for more. Why there is no FAQ? Because we are still discussing the meaning of a lot of terms I saw some posts on tentative glossaries of acronyms. Maybe before complex terms, we should focus on basic ones like universe. I would not be upset to encounter definitions for several possible senses of that word. Welcome, Thanks. Georges.
Re: Is the universe computable?
At 09:45 09/01/04 +0100, Georges Quenot wrote:
Bruno Marchal wrote:
At 11:34 08/01/04 +0100, Georges Quenot wrote:
I am very willing (maybe too much, that's part of the
problem) to accept a Platonic existence for *the* integers.
I am far from sure however that this does not involve a
significant amount of faith.
Indeed. It needs an infinite act of faith. But I have no problem
with that ...
Unfortunately, it seems that some people do.
It seems, but it isn't. Well, actually I have known *one* mathematician,
(a russian logician) who indeed makes a serious try to develop
some mathematics without that infinite act of faith (I don't recall
its name for the moment). Such attempt are known as ultrafinitism.
Of course a lot of people (especially during the week-end) *pretend*
not doing that infinite act of faith, but do it all the time implicitly. You
know an ultrafinitist cannot assert that he is an ultrafinitist without
going beyong ultrafinitism. So perhaps only animals do not do that
infinite act of faith, but IMO, most mammals does it in a sort of
passive and implicit way. If you pretend to understand a statement
like:
N ={1, 2, 3 ...}, or N = {l, ll, lll, ,
l, ll, lll, ...},
then you do it. Words like never, always, more, until, while, etc.
have intuitive meaning relying on it. I have worked with highly mentally
disabled people, and only with a few of them I have concluded that there
was perhaps some evidence in their *non grasping* of the simple
potential infinite. All finitist and all intuitionnist accept it. Second order
logic and any piece of mathematics rely on it.
Some people would like to doubt it but I think they confuse Arithmetical
Realism with some substancialist view of number which of course I reject.
(I reject substancialism even in physics, actually I showed it logically
incompatible with the comp hyp).
Fearing the death in the long run (as opposed of fearing some near catastroph)
also rely on that faith in the infinite, at least implicitly.
Some people believe that human are religious because they fear death, but
it is the reverse which seems to me much more plausible: it is because
we are religious (i.e. we believe in some infinite) that we are fearing death.
I am not sure how much I share that faith. As I mentionned,
I am willing to but since I could not find some ground to
support that willingness, I might be a bit agnostic too.
No problem. The point is that it is a nice and deep hypothesis
which makes comp fun and extremely powerful. It is definitely
among my working hypotheses.
snip
Why there is no FAQ? Because we are still discussing the meaning of
a lot of terms
I saw some posts on tentative glossaries of acronyms. Maybe
before complex terms, we should focus on basic ones like
universe. I would not be upset to encounter definitions
for several possible senses of that word.
I don't think the word universe is a basic term. It is a sort
or deity for atheist. All my work can be seen as an attempt to mak
it more palatable in the comp frame.
Tegmark, imo, goes in the right direction, but seems unaware
of the difficulties mathematicians discovered when just trying to
define the or even a mathematical universe. Of course tremendous
progress has been made (in set theory, in category theory) giving
tools to provide some *approximation*, but the big mathematical
whole seems really inaccessible. With comp it can be shown
(first person) inaccessible, even unnameable ...
Bon week-end,
Bruno
Re: Is the universe computable?
Bruno Marchal wrote:
At 09:45 09/01/04 +0100, Georges Quenot wrote:
Bruno Marchal wrote:
At 11:34 08/01/04 +0100, Georges Quenot wrote:
I am very willing (maybe too much, that's part of the
problem) to accept a Platonic existence for *the* integers.
I am far from sure however that this does not involve a
significant amount of faith.
Indeed. It needs an infinite act of faith. But I have no problem
with that ...
Unfortunately, it seems that some people do.
It seems, but it isn't. Well, actually I have known *one* mathematician,
(a russian logician) who indeed makes a serious try to develop
some mathematics without that infinite act of faith (I don't recall
its name for the moment). Such attempt are known as ultrafinitism.
Of course a lot of people (especially during the week-end) *pretend*
not doing that infinite act of faith, but do it all the time implicitly.
This is not what I meant. I did not refer to people not willing
to accept that natural numbers exist at all but to people not
wlling to accept that natural numbers exist *by themselves*.
Rather, they want to see them either as only a production of
human (or human-like) people or only a production of a God.
And I said unfortunately because some not only do not want to
see natural numbers as existing by themselves but they do not
want the idea to be simply presented as logically possible and
even see/designate evil in people working at popularizing it.
You know an ultrafinitist cannot assert that he is an ultrafinitist
without going beyong ultrafinitism. So perhaps only animals do not do
that infinite act of faith, but IMO, most mammals does it in a sort of
passive and implicit way. If you pretend to understand a statement
like:
N ={1, 2, 3 ...}, or N = {l, ll, lll, ,
l, ll, lll, ...},
then you do it. Words like never, always, more, until, while, etc.
have intuitive meaning relying on it. I have worked with highly mentally
disabled people, and only with a few of them I have concluded that there
was perhaps some evidence in their *non grasping* of the simple
potential infinite. All finitist and all intuitionnist accept it. Second order
logic and any piece of mathematics rely on it.
Some people would like to doubt it but I think they confuse Arithmetical
Realism with some substancialist view of number which of course I reject.
(I reject substancialism even in physics, actually I showed it logically
incompatible with the comp hyp).
I would not say infinite act of faith but rather act of faith
in infinity. I don't know the work of the mathematician you think
of neither of any other such kind of work but I flatly consider
that we only manipulate infinity formally within obviously finite
formalisms. I am not sure that it is necessary that any infinite
exists (let's say by itself in some platonic sense) for that
everything that we are talking abour within this kind of finite
formalism makes sense (and exists in some platonic sense).
Fearing the death in the long run (as opposed of fearing some near catastroph)
also rely on that faith in the infinite, at least implicitly.
Some people believe that human are religious because they fear death, but
it is the reverse which seems to me much more plausible: it is because
we are religious (i.e. we believe in some infinite) that we are fearing death.
I do not share all of Dawkins' views (especially from the social
point of view) but I have a Dawkins' view of religion. I would
say that human are religious simply because this induces among
themselves a behavior that increases their fitness (at the level
of communities). The corresponding set of memes interact in various
ways with other aspects like fear of death in complex networks
from which it might be vain to try to isolate simple one-way causal
relations.
I am not sure how much I share that faith. As I mentionned,
I am willing to but since I could not find some ground to
support that willingness, I might be a bit agnostic too.
No problem. The point is that it is a nice and deep hypothesis
which makes comp fun and extremely powerful. It is definitely
among my working hypotheses.
I think I can consider both this one and some alternatives
(not simulatneously, of course). However I do not find the
alternatives very fecund currently (and I am even more
agnostic about them).
Why there is no FAQ? Because we are still discussing the meaning of
a lot of terms
I saw some posts on tentative glossaries of acronyms. Maybe
before complex terms, we should focus on basic ones like
universe. I would not be upset to encounter definitions
for several possible senses of that word.
I don't think the word universe is a basic term. It is a sort
of deity for atheist.
I guess this would be called pantheism (the difference might
lie in the level of worship involved rather than in the level
of faith).
All my work can be seen as an attempt
Re: Why no white talking rabbits?
Hal Finney wrote: What about a universe whose space-time was subject to all the same physical laws as ours in all regions - except in the vicinity of rabbits? And in those other regions some other laws applied which allow rabbits to behave magically? While this may be possible, we seem to have found so far that the universe admits of many simple regularities in its complex systems and its fundamental laws. Therefore many of the essential properties (future-form-and-behaviour-determining properties) of these complex systems admit of accurate description by SIMPLE, SMALL theories that describe these simple regularities in the complex systems. I challenge you to come up with a simple, small, (thus elegant), and accurately explanatory theory of how space-time could be as you propose above, and also how this wouldn't mess up a whole bunch of other observed properties of the universe. My point is I don't think you (or anyone)'d ever be able to come up with a small, simple, yet explanatory theory of the white rabbit universe you suggest. AND THAT THEREFORE, at least according to how we've always seen the essential aspects of the universe conform to simple elegant theories and laws before, THE RABBITS SCENARIO (bizarrely strange yet still straightforwardly observable spacetime pockets) IS UNLIKELY TO BE THE TRUE STATE OF AFFAIRS in the universe. Could such a bizarre universe exist? Well possibly, (I personally think not an observable one), but in any case it would be a highly difficult universe (unmodellable with simple models) and physicists would be unemployed in that universe, as their predictions based on simple, clever theories would never turn out to work. Magicians and wizards (those able to pretend they'd been responsible for the last bit of observed extreme weirdness) would hold sway. Eric
Re: Is the universe computable?
Bruno Marchal wrote: I don't think the word universe is a basic term. It is a sort or deity for atheist. All my work can be seen as an attempt to mak it more palatable in the comp frame. Tegmark, imo, goes in the right direction, but seems unaware of the difficulties mathematicians discovered when just trying to define the or even a mathematical universe. Of course tremendous progress has been made (in set theory, in category theory) giving tools to provide some *approximation*, but the big mathematical whole seems really inaccessible. With comp it can be shown (first person) inaccessible, even unnameable ... Inaccessible in what sense? How do you use comp to show this? If this is something you've addressed in a previous post, feel free to just provide a link... Jesse _ Worried about inbox overload? Get MSN Extra Storage now! http://join.msn.com/?PAGE=features/es
Re: Why no white talking rabbits?
John Collins writes: I described a special case of this in a posting on this list a while ago, suggesting that we're almost certainly not in a simulated, 'second order' universe: Basically, for every arrangement of matter you could append to our universe that would look like some creature controlling/observing us, there would be many more arrangements that looked like no living creature. That's an interesting point, but I'm not sure it's correct. You might want to consider Nick Bostrom's Simulation Argument at www.simulation-argument.com as an alternative. I think the problem with your argument is that you are assuming that all physical arrangements of matter appended to the universe are equally likely. And in that case, you are right that some random arrangement would be far more likely than one which looks like an observer who has set up a computer to simulate our universe. However, I prefer a model in which what we consider equally likely is not patterns of matter, but the laws of physics and initial conditions which generate a given universe. In this model, universes with simple laws are far more likely than universes with complex ones. It seems plausible that our own laws of physics are not particularly complex. If string theory or loop quantum gravity or some other merging of QM and GR can work, we may well find that our entire universe is isomorphic to a few lines of mathematical equations. Similarly there are provocative hints that the initial state of the universe was extremely simple and had low complexity. These prospects lend support to my view, even though the universe contains objects of immense complexity. It's not the complexity of the universe that counts, it's the complexity of the equations that generate the universe. Consider a universe just like ours but where a given person is replaced by a random pattern of matter. Based on matter complexity, such a universe may seem more likely, since the structure of a human being is incredibly complex. But based on generative-law complexity, such a universe is much less likely, since it has a hole where the laws of physics did not apply, where what should have been a human being was artificially replaced by a random pattern. Therefore I'd suggest that when you consider the possibility that our universe is embedded in a larger structure, you can't just look at the matter complexity of that structure. Rather, you should look at the physical-law complexity. And it seems plausible to me that the physical laws of the outer universe don't necessarily have to be much more complex than our own. In fact, it may be that we are capable of simulating our own universe (we don't know the laws of physics well enough to answer that question, IMO). Nick Bostrom proposes in effect that the outer universe could be the mathematically identical to the inner one. He also suggests that there could be many simulations running, so that the number of observers in the simulated universes is far greater than the number in the outer universe. Based on this reasoning, the likelihood of our being in a second-order simulated universe is very considerable and can't be ruled out. Hal Finney
Peculiarities of our universe
There are a couple of peculiarities of our universe which it would be nice if the All-Universe Hypothesis (AUH) could explain, or at least shed light on them. One is the apparent paucity of life and intelligence in our universe. This was first expressed as the Fermi Paradox, i.e., where are the aliens? As our understanding of technological possibility has grown the problem has become even more acute. It seems likely that our descendants will engage in tremendous cosmic engineering projects in order to take control of the very wasteful natural processes occuring throughout space. We don't see any evidence of that. Similarly, proposals for von Neumann self reproducing machines that could spread throughout the cosmos at a large fraction of the speed of light appear to be almost within reach via nanotechnology. Again, we don't see anything like that. So why is it that we live in a universe that has almost no observers? Wouldn't it be more likely on anthropic grounds to live in a universe that had a vast number of observers? The second peculiarity is the seemingly narrow range of physical laws which could allow for our form of life to exist. Tegmark writes about this at http://www.hep.upenn.edu/~max/toe.html. He shows a chart of two physical constants and how if they had departed from their observed values by even a tiny percentage, life would be impossible. In the full paper linked from there he offers many more examples of physical paramters which are fine-tuned for life. So why is this? Why does it turn out that our form of life (or perhaps, any form of life) can exist for only a tiny range of variation? Why didn't it turn out that you could change many parameters a great deal and still have life form? I don't see anything a priori in the AUH that would have led to this prediction. Now, it may just be one of those things that happens to happen, a fundamental mathematical property like the distribution of primes or the absence of odd perfect numbers. Self-aware subsystems just mathematically turn out to only be possible in a very tiny region of parameter space. Now, you might be able to make the argument that tiny is not well defined, that there is no natural length scale for judging parameter ranges. Tegmark could as easily have zoomed in on the appropriate region of his graph and shown a huge, enormous area where parameters could be moved around and life would still work. However I think there is a more natural way to put the question, which is, what fraction of computer programs would lead to simulated universes that include observers? And here, if we follow Tegmark's ideas, the answer appears to be that it is a very small fraction. (Of course, you still need to use your own judgement to decide whether that is tiny or not.) In a way, then, these two questions are both related, and perhaps the same. They both ask, why so few observers? One question looks around the interior of our universe, and the other looks at the set of all universes. In each case, it seems that intelligent life is terribly uncommon. Hal Finney
Re: Why no white talking rabbits?
Chris Collins wrote: This paradox has its origin in perception rather than fundamental physics: If I fill a huge jar with sugar and proteins and minerals and shake it, there is no reason why I can't produce a talking rabbit, or even a unicorn with two tails. Yet out out of the vast menagerie of novel objects and creatures I could produce, I always seem to get a bubbling cloudy liquid. The solution, of course, is that there is an even larger menargerie of objects, all of which look the same to me (like a bubbling cloudy liquid, in fact). This is exactly why I suggested the white rabbit example was misleading, and that it would be better to focus on an example where the number of possible outcomes predicted by physical laws is much *smaller* than the number of logically possible outcomes, like in the double-slit experiment. Similarly, there is no reason ehy such object, could not appear out of the quantum vacuum, but it must be the case that this vacuum throws up a lot of different objects and events that look to us like 'empty space' and 'nothing happening' (although I suspect that the case of the paradox you give of the double slit experiment has its origins in considering too large a set of states as 'possible'; the positions of the photons are not really free variables, with the apparently 'artificial' physical laws following from the initial data. It's like asking why the pegs on my washing line always follow the 'coshine law'...). What do you mean by not free? Surely if the everything that can exist, does exist hypothesis is true, then for every possible pattern of photons hitting the screen, there is a reality where some version of you experiences exactly that pattern when he does the experiment (a version of you that has no memory of any previous violations of the laws of physics, mind you). Thus you really need some kind of measure, either on possible universes or possible observer-moments, to justify the belief that you have a very low probability of experiencing one of these outcomes. You can't just take the probabilities predicted by the laws of physics for granted, if you believe in the existence of universes/observer-moments where these laws can change. Jesse _ Have fun customizing MSN Messenger learn how here! http://www.msnmessenger-download.com/tracking/reach_customize
Re: Why no white talking rabbits?
Hal Finney wrote: I think the problem with your argument is that you are assuming that all physical arrangements of matter appended to the universe are equally likely. And in that case, you are right that some random arrangement would be far more likely than one which looks like an observer who has set up a computer to simulate our universe. However, I prefer a model in which what we consider equally likely is not patterns of matter, but the laws of physics and initial conditions which generate a given universe. In this model, universes with simple laws are far more likely than universes with complex ones. Why? If you consider each possible distinct Turing machine program to be equally likely, then as I said before, for any finite complexity bound there will be only a finite number of programs with less complexity than that, and an infinite number with greater complexity, so if each program had equal measure we should expect the laws of nature are always more complex than any possible finite rule we can think of. If you believe in putting a measure on universes in the first place (instead of a measure on first-person experiences, which I prefer), then for your idea to work the measure would need to be biased towards smaller program/rules, like the universal prior or the speed prior that have been discussed on this list by Juergen Schimdhuber and Russell Standish (I think you were around for these discussions, but if not see http://www.idsia.ch/~juergen/computeruniverse.html and http://parallel.hpc.unsw.edu.au/rks/docs/occam/occam.html for more details) Therefore I'd suggest that when you consider the possibility that our universe is embedded in a larger structure, you can't just look at the matter complexity of that structure. Rather, you should look at the physical-law complexity. And it seems plausible to me that the physical laws of the outer universe don't necessarily have to be much more complex than our own. In fact, it may be that we are capable of simulating our own universe (we don't know the laws of physics well enough to answer that question, IMO). If the everything that can exist does exist idea is true, then every possible universe is in a sense both an outer universe (an independent Platonic object) and an inner universe (a simulation in some other logically possible universe). If you want a measure on universes, it's possible that universes which have lots of simulated copies running in high-measure universes will themselves tend to have higher measure, perhaps you could bootstrap the global measure this way...but this would require an answer to the question I keep mentioning from the Chalmers paper, namely deciding what it means for one simulation to contain another. Without an answer to this, we can't really say that a computer running a simulation of a universe with particular laws and initial conditions is contributing more to the measure of that possible universe than the random motions of molecules in a rock are contributing to its measure, since both can be seen as isomorphic to the events of that universe with the right mapping. Jesse Mazer _ Get reliable dial-up Internet access now with our limited-time introductory offer. http://join.msn.com/?page=dept/dialup
Re: Peculiarities of our universe
- Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, January 09, 2004 3:24 PM Subject: Peculiarities of our universe There are a couple of peculiarities of our universe which it would be nice if the All-Universe Hypothesis (AUH) could explain, or at least shed light on them. One is the apparent paucity of life and intelligence in our universe. This was first expressed as the Fermi Paradox, i.e., where are the aliens? According to the anthropic principle, all conditions are such that our existence is possible. Also, all events up until now have been such that they favored our existence. This doesn't necessarily mean that those events were probable. In fact, they could have been wildly improbable. (that asteroid killing the dinosaurs at just the right moment might have helped us) Let us say you're repeatedly throwing a thousand dice on the floor, and that you are waiting for a pattern of fifty sixes to group close together on the floor. When they finally show up, it's doubtful that another distinct group of fifty sixes will show up in the same throw. In this analogy, the floor and dice represents (roughly) *this* universe and its galaxies and stars, and the groups of fifty sixes represent planets harboring intelligent life. After all, we seem to be very, very complex creatures. Most of the matter in the universe looks quite disorganized in comparison. Wouldn't this intuitive analogy explain why life is so rare ?
Re: Why no white talking rabbits?
Jesse Mazer wrote: Why, out of all possible experiences compatible with my existence, do I only observe the ones that don't violate the assumption that the laws of physics work the same way in all places and at all times? There are two kinds of white rabbits: microscopic and macroscopic. Microscopic white rabbits exist all around us. Particles popping in and out of the vacuum, particles being two places at the same time and so on. Microscopic white rabbits obey statistical rules, distributions etc, which translate into very solid and reproducible macroscopic laws such as the second law of thermodynamics. Because of these solid macroscopic laws, macroscopic white rabbits are extremely rare. The macroscopic laws of physics are the same everywhere because mathematics (statistics) is the same everywhere. In the multiworld context one could say that each multiworld branching is a white rabbit, but these rabbits are too small to notice classically. Thus, overall the number of worlds not containing macroscopic white rabbits is much larger than those containing macroscopic white rabbits. Therefore the transition from one world to the next is extremely unlikely to display a macroscopic white rabbit. Ergo: No observable macroscopic white rabbit. But of course the biggest rabbit is taken for granted. It is right under our nose and so close that we don't see it. George Levy
