I merely said that it seems that computationally universal rules are the norm, which is supported by, for instance, the investigations Stephen Wolfram has led into some of the simplest rulesets imaginable.
Well, that depends on what you mean by complexity – one could say, for instance, that all evolutions of computationally universal systems are of equivalent complexity, as every such system can emulate every other.
If things were sufficiently different, then we just wouldn’t know. Sure, we wouldn’t get carbon-based sentient meat, but who knows what we’d end up with? – Of course, ‘who knows’ isn’t a very good argument; but, if you were given the laws of our universe, knowing nothing of its structure otherwise, do you think you’d be able to easily divine whether or not this universe could harbour sentient observers?
Anyway, this is straying rather far from the topic; if you want to debate this somewhere else, I’d be happy to join (though I’m not sure how much spare time I’ll have in the near future). For this thread, we should probably wait and see how and if the OP weighs in on the subject, and what he has to say on the answers provided so far.
FWIW I thought your initial response was the most to-the-OP’s-point post, and it gave me some good leads, so thanks.
Does anyone know: Is there some non-zero probability to be assigned to a situation in which things are just exactly as they are up to a point in the very near future, and then all of a sudden gravity just apparently stops working? If this is physically possible in some strict sense–i.e. if it’s compatible with everything we know about how the world works–then AFAICT the logical and physical possibilities are the same after all. (I’m asking about this because in my line of work at least its usual to draw a distinction between these two kinds of possibility. However, it may not be that important of a point–perhaps “physical possibility” could be interpreted to mean “probable to within a certain degree” or something along those lines.)
The multiverse model if I understand correctly says there is indeed a universe just like this one but in which at some point, gravity simply apparently stops working. Outside a multiverse model, if I understand correctly, the very same facts about (what we know about) waveforms lead us to the conclusion that there’s an incredibly small but non-zero probability that the waveform of the universe might end up collapsing that way.
Have I got it all wrong though?
(Regarding logical possibilities that are physically impossible: Some people argue that “X is both red and green” is logically but not physically possible, because “X is red” is not in logical contradiction with “X is green” unless you throw in “Nothing has two colors.” So, the argument goes, just build a possible world in which you’ve got facts about things having colors, but the proposition “nothing has two colors” is false, and you’ve got a model for “X is both green and red.” Not physically possible, but logically possible. But I’m not sure it’s logically possible–I’m not sure whether you could actually be talking about colors if you’re talking about something that a single object could have more than one of in the same place at the same time. Ahem setting aside the problem that “color” is a pretty complicated predicate, really, relying not just on properties of things but their relations to other things including the human perceptual system etc… you could probably run the same argument on something like “charge”.)
I was going to ask some similar questions. Namely:
[ul]
[li]Are you asking whether it could’ve been possible for the speed of light to be something other than approximately 186,282 miles per second?[/li][li]Are you asking whether it could’ve been possible for pi to be something other than approximately 3.14159265?[/li][li]Are you asking whether it could’ve been possible for the intensity of light to be something other than inversely proportional to the square of the distance?[/li][/ul]And: Are the above questions related to each other, or are they independent of each other?
Are there really people who argue that? I’d think that “X is red” and “X is green” are meaningless statements unless “red” and “green” are predefined. And then, once they have been defined, “Nothing has two colors” is automatic and superfluous. And therefore, they are in logical contradiction from the beginning.
That is not at all supported by the investigations of Stephen Wolfram. Yes, he found computationally universal rule sets. But he didn’t find that they are “the norm.” Nor did he show that computationally universal rule sets are in any way likely to harbor complex organisms from arbitrary initial conditions. In fact, the known laws of physics are known to be very unlikely to support life if it weren’t for spectacularly fine-tuned low-entropy initial conditions.
You have it mostly right, but not quite. First of all, I think you mean “many worlds interpretation” when you say “multiverse model.” Be careful about confusing those two, because they are very different things. Second of all, in whatever interpretation of quantum mechanics you choose, gravity never “stops working.” A particle can, however, “tunnel”, across a gravitational barrier. But this cannot be logically interpreted as the same as “gravity having been turned off for this one particle for a brief period” because the kinetic energy of the particle is changed by the correct amount of gained/lost potential energy, among other things.
I was going to ask some similar questions. Namely:
[LIST]
[li]Are you asking whether it could’ve been possible for the speed of light to be something other than approximately 186,282 miles per second?[/li][/quote]
This is something I’d be curious about.
[quote]
[li]Are you asking whether it could’ve been possible for pi to be something other than approximately 3.14159265?[/li][/quote]
Not really this–it’d be logically impossible for the value of the ratio between the diameter and the circumfrence of a circle in a flat euclidean space to vary.
[quote]
[li]Are you asking whether it could’ve been possible for the intensity of light to be something other than inversely proportional to the square of the distance?[/li][/quote]
Hrm… maybe I didn’t understand you though I thought I did.
Are you saying it’d be physicall impossible–not just incredibly improbably but impossible–for things to suddenly begin proceding as though there were no gravity? For example, massive objects would stop following curved paths around each other, etc. This isn’t just improbable, but physically impossible–not occuring in any of the many world worlds, not occuring according to any way the waveform of the universe might collapse?
If that’s so, the answer to my question would be “no–some logical possibilities are physically impossible.” Unless for some reason the existence of a force of gravity is logically necessary.
At a fundamental level, it’s impossible for us to infer from empirical observations about this universe a logical conclusion about “other universes”, or even other parts of this universe. Just because we have never yet seen a physical law change in such a profound way as “gravity stops working” does not mean that it might not happen. It is in a strict sense logically invalid to assume that empirical observations will be consistent over time. There are some underlying logical rules about science that are there as a practical matter, otherwise nothing could ever be accomplished.
Or so I aver. This is really more of a philosophical question about the nature of science itself. Some may believe that the strong correlation between mathematics and physical laws means that we really are discovering logical facts about how the universe works. My opinion is that you can’t use the one to prove the other, no matter how hard you try.
Hmm. Couple things: Probability does some non-intuitive things when it comes to infinities (as almost anything does), such as the (presumably) infinitely many ‘possible universes’/‘histories’ whatever you’d want to call them, such that, for instance, one might have to assign a probability of zero to something that still, in principle, could happen – if there’s for instance just one history (or finitely many histories) in which it occurs. The reason for that is that, roughly, it doesn’t make much sense of choosing this history with a probability of ‘one over infinity’; technically, one refers to measure theory to deal with this sort of stuff, in which such finitely many out of infinitely many possibilities are called a measure-zero set.
Anyway, that isn’t really to the point. As for whether or not gravity could suddenly, physically, ‘turn off’, sure it could – for instance, Newton’s constant could turn out not to be constant after all, and instead vary with time, such as the fine-structure constant (which roughly measures the strength of the electromagnetic interaction) has occasionally been theorized to do, and just go to zero very fast at some point – I don’t know that it’d be especially easy to formulate such a model, but I can’t think of any reason it should be impossible, either.
In fact, varying or ‘running’ coupling constants are nothing extraordinary in contemporary physics – compare it to the behaviour of the coupling constant of the strong nuclear force, which asymptotically approaches zero when going to high energy.
However, why do you think it’s logically possible for gravity to suddenly vanish? Sure, you could imagine it happening, but that only tells us you have a vivid imagination, nothing about logical possibility – all propositions you care to utter are predicated on the state of the universe, and it might well be that this state (as it is now) contradicts gravity turning off any time in the future; in other words, it might well be that ‘if gravity exists now, it will always exist’ is true, thus making ‘gravity will cease to exist at some point’ a logical impossibility, the same way the truth of ‘Socrates was a man’ makes it impossible for ‘Socrates was a woman’ to be true. No?
Well, they certainly are very common, at any rate; even the simplest set of rules, 1D cellular automata, contains at least one example, and their frequency tends to increase the more complicated the underlying rules become. He’s certainly argued that most systems are computationally universal, if perhaps not exactly proved it.
It’s at least as likely as a random computation yielding a normal number, which, since almost all numbers are normal, is pretty likely. (Though it occurs to me that I don’t know if that holds for computable numbers.)
Really, I think we’re talking past each other. I’m not talking about life, or anything that would look in any way familiar – merely about complexity, or perhaps about information-processing capacity.
Perhaps, but keep in mind that I have been responding to this post in which it seems pretty clear that you are talking about more than just complexity – you are talking specifically about the anthropic principle – self-aware complexity. Information processing capacity is very different indeed from the likelihood of encountering self-aware substructures…
According to the known laws of physics, what you are describing is physically impossible (not merely unlikely). The reason why is because the situation you are describing does not locally conserve energy. Even in quantum mechanics, energy must always be conserved. Note that other “weird” things are possible; for example your cup of coffee can “tunnel” through the table it’s sitting on and still conserve energy. But you could never “watch” the cup moving against gravity, since doing so would imply collapsing the wave function of the cup to non-virtual states that violate conservation of energy.
For a more clear example, consider the wave function of the electron orbiting an atom. For some orbitals (such as the p orbital) the electron’s wave function is zero at x=0. Not just a small number. Exactly zero. There is no universe in which the electron can be at x=0, and there is zero probability of it ever being at zero. I suppose you could argue that the electron being at x=0 is a generic logical possibility (even though it is not a logical possibility within the theory in question).
So the answer to your question is no – some logical possibilities are physically impossible, if by physically impossible you mean not allowed by the known laws of physics.
Hm, do you use different terminology than I am familiar with? To me, the Game of Life is a 2d automaton, and it’s certainly universal…
I’m very careful in saying things like ‘in principle’ and ‘can yield complexity as great as…’; I’m really not sure where, exactly, I stepped on your toes with that.
But, as I’ve already said, there’s an issue here about how to define complexity. All universal systems are equivalent to one another, thus, one’s output, which we can for example think of as a string of bits, can computably be translated into any other’s. They contain the same information, in the sense that there is a Turing machine such that, if it is given one of the bit-strings on its input tape, it will produce the other on its output tape. So if one, say, corresponds to a simulation of out universe and hence contains self-aware structures, doesn’t the other, as well?
Not sure this is quite right. A quantum particle’s wave function in a gravitational potential is given by the Airy function, which is non-zero for any z > 0 (though it gets very close to zero very quickly). So there’s a non-zero probability to observe the particle at any height.
Anyway, quantum tunneling isn’t the only possibility for a catastrophic loss of gravity; and if I read Frylock correctly, he doesn’t seem to be interested in physical possibility as given by laws of physics as they are currently understood, but rather, as given by universes whose history does not differ from our own physically up to the now, but diverges afterwards, which is a vastly larger class and certainly merits being called ‘physically possible’ IMHO.
And I’m still not sure if ‘logically possible’ isn’t tossed around a bit carelessly in this thread. You might, for instance, model the universe as a set of propositions, with which each ‘logically possible’ proposition would have to be at least compatible; the apparent logical possibility of something might then be nothing more than an expression of our ignorance.
… and it’s a notable exception. It’s well known that universal 2d automatons are perversely rare.
You said “from that viewpoint, strong forms of the anthropic principle seem rather spurious right off the bat.” I was pointing out that your “viewpoint” (ie premise) was wrong. Calling something “spurious right off the bat” is not being “very careful” IMO. The sentences previous to it were couched in some “careful” wording, but it seems rhetorical of you to act as though you don’t know what I am talking about. You said “the anthropic principle seem rather spurious right off the bat” because of the supposed commonness of universal computability. I am saying 1) it’s not that common, and 2) commonness of computability is irrelevant – commonness of viable initial conditions is paramount.
Yes. I don’t see how this is relevant to our previous discussion, or where you are going with this…
Energy is always conserved between measurements, but energy and position are not always certain. More concretely, for a particle in a potential well, one can measure its position or its momentum, but not both simultaneously. The exponentially decaying part of the Airy function reflects this fact – for well defined energy eigenvalues, position is rather uncertain. And yet it is both the position and the momentum of the particle in the well that allows one to determine whether energy has been conserved between measurements. Suppose you measure the particle to be in the lowest energy state at time t1. If you repeat the measurement at time t2, the particle will be in the same energy state, because energy is conserved. But if, at time t3, you attempt to measure the position of the particle in the well, you run into trouble – according to the Airy function, you may measure the particle to be in a classically forbidden region. But aha, you didn’t violate conservation of energy… why? Because by collapsing to a position eigenfunction you have lost your energy certainty – now you have a spread of energy eigenvalues. Therefore if, at time t4, you repeat the energy measurement, you may not measure the same energy as you did before. But how is this possible? Because by measuring the position of the particle, you interacted with the environment. The change in energy between measurements at time t1 and t4 is compensated by a corresponding absorption or lost of energy by the measurement apparatus. The point is that energy is always conserved. The universe’s wave function, including both the measurer and the measured, always conserves energy between measurements. There is no way around this. There is no universe, no quantum probability, that you will ever find a closed local quantum system to violate energy conservation. Quantum mechanics does not allow “every logical possibility.”
The above is subtle. But again, we might as well take something simpler, like electron orbitals, as an example. Even the Airy function has “zeros”. There are plenty of solutions to schrodinger’s equation that have points of absolutely zero probability. The probability for an electron to decay to a muon has zero probability, etc etc…
I agree that it hasn’t been made totally clear by Frylock how he defines both “physically possible” and “logically possible.” For the sake of discussion, I have been using:
physically possible = consistent with the known laws of physics
(ie, me spontaneously teleporting to the other side of the earth is physically possible)
(but an electron decaying to a muon in isolation is not physically possible)
logically possible = something that can be imagined to occur if one gets to choose the rules
(ie there is nothing inherently illogical about an electron decaying to a muon – it is logically possible)
Granted. But, as you seem to acknowledge in calling their rareness ‘perverse’, that’s an uncommon situation.
From that viewpoint – I’ve essentially posed an argument, and then said ‘if that’s true, then complex observers aren’t so special after all’. You disagree with the argument – that’s fine. I’m just not sure why that latter part should elicit such a comparatively strong response from you.
Well, it illustrates that computational universality does suffice; there’s no mention of initial conditions or fine tuning. Basically, you grab a rule out of the bag of possible rules, and with some luck, it’ll be universal. The evolution this rule leads to then is as complex as our universe, fine-tuned and all (as again there exists a TM that reproduces our universe’s evolution from the rule’s evolution).
I didn’t claim that QM doesn’t conserve energy (and besides, position eigenstates of a particle in a gravitational potential have a definite energy = mgz, so if I measure the particle at some definite position and hence ‘collapse’ the wave function into a position eigenstate, there’s no energy uncertainty). Just that it is indeed possible to observe a quantum object in a state in which it classically, obeying gravity, could not be, and hence, have the appearance of gravity turning off.
That seems like a rather empty definition to me, because then, everything is logically possible. (After all, I could always choose the rule that ‘x is possible’ for any x!)
The fact is that no one has shown that computability is common or uncommon. You can find examples where computability is common, you can find examples where it is uncommon.
I don’t think my response has been particularly strong. If it has been, it is only because you keep responding defensively about my behavior as perceived by you, rather than just sticking to the point. All I’m interested in is the discussion, not whether or not my responses are overly strong. Harping on the point, as you do, is irritating. Let’s stick to the interesting stuff.
Suffice for what? Seriously, you aren’t explaining yourself well enough here. Just because a rule is universal doesn’t mean that there is ‘software’ to generate self-aware complexity. You can have a universal rule in which for 99.99999999% of initial conditions everything (to use an analogy) collapses into a black hole, or produces ‘blinkers’ (referring to Conway’s game of life), etc. Initial conditions are extremely important, regardless of isomorphisms between different rule sets.
No. You are forgetting about the momentum of the particle.
