Conservation Of Information?
Posting again on a subject I don't understand and never will: what physicists mean by "information." My brain balks at mathematical symbols, but I'm good at concepts; so my guess is that if some articulate physicist were to wander by, he or she could explain "conservation of information" in a way that doesn't totally leave me at sea. Wikipedia hasn't succeeded*, but this passage from the entry on "Black hole information paradox" is useful:
There are two main principles in play:
--Quantum determinism means that given a present wave function, its future changes are uniquely determined by the evolution operator.
--Reversibility refers to the fact that the evolution operator has an inverse, meaning that the past wave functions are similarly unique.
The combination of the two means that information must always be preserved.
What I gather from this is that: (i) any present "state" must have a unique past; you can't have two pasts leading to the same present; and (ii) the present can't lead to multiple futures. Am I interpreting this right? So a quantum waveform (?) version of a Laplace Demon** could reconstitute the past or forecast the future (or maybe, this being quanta, could reconstitute past probability wave something-or-other and forecast future probability wave something-or-other) based on what's known now. Hence information is preserved. So, however you twist it, you'll always have the same information.
When people talk about, say, "conservation of energy," I assume they mean that the amount of energy stays the same, no matter what form it takes. Whereas if someone says "conservation of information," I'd think (or guess, anyway) that what is meant isn't just that the amount of information is constant but that any form ("form"?) the information has taken can be reconstructed and whatever form it will take can be foreseen.
(Are reconstructing and foreseeing identical operations? If they're not, I don't understand how information can be said to be conserved. But then, as I say, I don't know what physicists mean by "information," or if they agree about what they mean by "information.")
This is not intuitive, but what's to come is even less so.
Black holes seemed to pose a problem for the principle in that, whatever you put into a black hole, you'd get the same result, a black hole that eventually irradiates away. (Is that the right way to put it, "irradiates away"?) So different pasts produce the same future; the same future can have more than one past. So that particular future doesn't preserve information about its actual, unique past. Currently, Leonard Susskind and crew believe they've definitively resolved the problem in favor of conservation of information, i.e., the preservation of a unique past, the resolution being by way of the holographic principle, though not everyone is convinced. I won't go into any of that yet.
The question I posed last time is, "When physicists say that information is preserved even after everything's been absorbed into black holes that have subsequently evaporated, do they mean that, e.g., 'The test tomorrow is at 1:00 PM' is preserved?" Certainly in my everyday use of the term "information," "the test tomorrow is at 1:00 PM" is information. So I can simplify my question down to this:
Is "The test tomorrow is at 1:00 PM" preserved (by the principle of conservation of information)? If not, what is preserved?
For some reason, I felt ("felt") last time that the answer to the first question was "No, 'the test tomorrow is at 1:00 PM' is not preserved." I had a sense that what the physicists meant was some broader numerical something-or-other about the "state," not specifics such as "The test tomorrow is at 1:00 PM" or "The Sun has eight planets and scads of minor planetoids." Now I'm tending to think ("think"?) the opposite. If physical information is preserved/conserved, this includes, "The test tomorrow is at 1:00 PM."
I continue to have little idea what I'm talking about. But right now I'd reformulate the question as:
If all physical information is preserved, how can "The test tomorrow is at 1:00 PM" not be preserved?
And a corollary to that one would be:
If all physical information is preserved, and this - somehow - does not include "The test tomorrow is at 1:00 PM" being preserved, then how is it possible that "The test tomorrow is at 1:00 PM" exists even now?
So, to convince myself that all information can be preserved while "The test tomorrow is at 1:00 PM" is not preserved, I'd have to have an explanation for why "The test tomorrow is at 1:00 PM" isn't preserved. And to do that, I'd have to have an explanation for how it can exist now without being physical information. We as physical beings sure seem to have the information that the test tomorrow is at 1:00 PM. So far I can't counter this, can't come up with an explanation of how physical beings can have nonphysical information, or what "nonphysical information" would even mean. I don't think physicists, to the extent that they've thought about it, disbelieve that "mental" and "cultural" information can be conveyed by physical information, or that the latter two sorts of information are different in kind from the former. Actually, I don't know what they think. But how would they even potentially explain the existence of "cultural information" at all if such information is not conveyable physically?
That's what I would need to explain, if I wanted to preserve the principle of "conservation of information" while denying the conservation of "The test tomorrow is at 1:00 PM." Not that I necessarily want to deny that "The test tomorrow is at 1:00 PM" can be preserved. What I'm saying is that I don't know how not to preserve it without destroying the principle of conservation of (physical) information - which for all I know is a wrong principle, but to half understand what physicists mean by it, I'm acting as if it's right. Quantum physics guys seem to believe it needs to be right. So, for the moment at least, I'm counting "The test tomorrow is at 1:00 PM" as physical information, hence preservable by "conservation of information."
So, to reiterate, I think the crucial question here, this time in bold, is: How can "The test tomorrow is at 1:00 PM" exist now without being physical information?
I'm deciding for the time being that it can't, and that therefore it is physical information.
In our last episode, arbitrary_greay was playing with contrary ideas, drawing a distinction that I probably don't understand:
Best I can guess is to think in programming terms: at the high-level language stage, variables are given names, and when searching for a piece of data stored in a variable, you call its name, which therefore is dependent on its descriptor. Searching the wrong descriptor will give you the wrong variable, and thus the wrong data.
However, at lower levels, compiler and binary languages, the descriptor is only used as a reference to a location. The data in that location does not change regardless of what descriptor is used to simply "remember" where that location is. I'm guess that "information" is referring to the data (the state of being), not the name given to the location.
AG continues in a later comment,
But the reconstruction of neurons and synapses constructs the words and relations between them in "The test tomorrow is at 1:00 PM," not the location of the earth. The reconstruction of "The test tomorrow is at 1:00 PM" is not necessary to the reconstruction of the location of the earth, which would happen independent of any particular evolution of neurons and synapses. That's what I personally mean when I differentiate being "objects in and of themselves" and being a reference to something else, and why a phrase as a linguistic construct is preserved, but not the phrase as a description of something.
Like in programming: the name given to a variable is itself stored as a series of 1s and 0s (or at the physical level, two different phases of silicon) somewhere on a chip. That is conserved. But when we consider it as a pointer to where some other data is, that data is conserved, and not the pointer.
And that's where we left it.
While I agree that one can know the location of the Earth without knowing that the test tomorrow is at 1:00 PM, I don't agree that, if reconstructing the location of the Earth is the result of conserving all physical information, that reconstructing "The test tomorrow is at 1:00 PM" isn't also the result of conserving all physical information. The mechanism that would give us one piece of information would have to give us the other as well. Or if it doesn't, there has to be an explanation of why not, and I can't think of one.
Even if it's true that the Earth would have had a location without the evolution of neurons,*** this is no more significant than that my grandma would have been born even if later on I hadn't been. That doesn't make me any less reconstructible than her, despite my dependence on her and her independence of me. If conservation of information preserves the location of the Earth, it preserves neurons and synapses, and Russian, and me, and English, and how to use it.
And my second way of putting this is: if all "physical information" can be preserved without preserving English and how to use it, then there can be no good way to explain how physical beings right now have and use English. If a future that preserves all physical information can't figure out what a pointer points at, then neither can we. (This is just a more general way of saying what I said above about "The test tomorrow is at 1:00 PM" being preserved if all physical information is preserved.)
AG seems to be distinguishing between, on the one hand, location and the words that designate it (both the location and the words can have a physical existence) and, on the other, the connection between the words and what they designate, which supposedly doesn't have a physical existence, but rather is set by convention. Whereas I'm arguing that if we, now, physical beings, can connect words and what they designate, then, if all physical information about us is preserved, the connections we make between words and what they designate are also preserved, are also contained within the physical information. Otherwise, how is information informative?
The principle seems either/or to me: either some physical beings can use English, in which case their use of English is preserved along with all other physical information that's preserved by the principle of conservation of information, or not all physical information is preserved/conserved.
[EDIT: When I say "the connections we make between words and what they designate are also preserved, are also contained within the physical information," I don't mean the connections are contained as separate pieces of information, the words and what they designate here, and the connections there. See the comment thread for elaboration (here and here).]
I realize that our experience with fossils and archaeology tends to leave us with bones and markings from which we can at most infer behavior and language, meanings, etc. But then, we don't pretend that paleontology and archaeology give us all the information there is.
But anyway, I'm not yet claiming to understand "conservation of information," what it means. It seems unclear to me as a coherent principle. As Mark says, in brackets (the final statement in the second bracket seeming to contradict all that came before):
[posts above have raised the issue that information in physics terms is not necessarily "communicable" -- as it must be for eg Claude Shannon -- bcz it doesn't require the presence of beings that can "read" the information <--- which is an interesting aspect of the problem, but not one that mathematicians and cosmologists spend much time on; they tend to operate as "under god's eye" communications theorists, even when militant atheists; the information that is an object's waveform structure is deemed "objectively readable" even if no one is EVER going to be around who can actually read it] [for maths and physics this is a side-issue however: information in the social sense is very much NOT conserved, vast amounts is lost everytime someone dies -- the mathematical ideal is that, if the full picture of all waveforms could be retrieved, then ALL information, including the fleeting never-spoken thoughts of the long-dead, could be reconstituted, indeed the retrieval and the reconstitution would kind of be the same activity]
My guess now (as opposed to a couple of months ago) is that the Susskind types would believe that information in the social sense is indeed preserved. They damn well ought to, anyway, because otherwise they ought to contend that information in the social sense doesn't exist now, either.
To think otherwise would put language in a spirit realm beyond the reach of physics, biology, and understanding. Or, anyway would put it somewhere beyond physics and biology. (Are there neo-this-ists and neo-that-ists who believe that reason itself has an existence beyond physics and biology and evolution? And are there people who still believe in Cartesian "mind stuff" (if that's what Descartes believed [I don't remember if I reached that part in my reading of Descartes]? I can't say I'm well read in either old or current philosophy.)
I'm going to guess (without knowing) that Sean Carroll and Leonard Susskind and those types would actually not accept that "an object's waveform structure is... [merely] 'objectively readable' even if no one is EVER going to be around who can actually read it." And I'm kind of hoping, therefore, that they won't accept that social information is lost when someone dies. The dead person's "social" information should be as preserved and reconstructible as any other information. What I'm guessing they would not accept are (1) that it's okay to make your system work by positing a hypothetical but nonexistent entity that "could" read the information, a Laplace Demon of the waveforms or a god or some such (rather, your system needs to function on its own, without adding something imaginary to it; or what you've added must have physical attributes, which you then have to take into account and explain as part of the system, the explanation including how it physically got there); and (2) that the ability to read information is not itself information. In case my double-negative sentence structure is confusing I'll state these in the positive: these quantum physicists should believe that (1) You don't need to assume (and aren't allowed to assume) a god's-eye view or a special Laplace Demon of the waveform because (2) the ability to read the information is information itself and is therefore preserved along with the (rest of) the information. Conversely, if at the end you have to introduce something else, from outside your system, then the information hasn't been conserved. I'll append a (3) which is a variation on (1): "objective" and "subjective" are not terms within quantum physics (you don't talk about "objective quarks" and "subjective quarks," or conduct calculations with the terms "objective" and "subjective"), even if "objective" is a term that some people use to compliment results of quantum physics that they agree with and think are established. So the phrase "objectively readable" has no explanatory power, and can't be called in to make a physical theory work.****
(I do have a question that belongs here, but I won't say it right off.)
So what I'm wanting those quantum physicists to assume (what would seem consistent) is that skills - including the ability to use information, to read it, to understand "The test tomorrow is at 1:00 PM" - are themselves information and are preserved along with all other information. So the information that is preserved includes the aforementioned ability of the information to read and understand itself.*****
Of course, this seems totally absurd, that after every piece of matter is absorbed into black holes that subsequently evaporate, nonetheless we have information left that can read and interpret itself. It's as if we've been made immortal.
But of course, maybe it's equally absurd that we can read and interpret information now, though we most assuredly can. And the fact that we can read and interpret information now is the linchpin of my argument (to the extent I've got an argument).
But I'm not sure (not understanding physics) that the holographic principle doesn't appear equally absurd, in the exact same way as information's ability to read itself appears absurd. And though the holographic principle may turn out to be wrong, it's not being dismissed out of hand by physicists. Of course I don't come within a million and one miles of pretending to understand the holographic principle. What I gather about the holographic principle, though, is that (saith Wikipedia, speculatively) "the entire universe can be seen as a two-dimensional information structure 'painted' on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies." So the holographic principle isn't saying we are represented by a two-dimensional information structure on a two-dimensional cosmological horizon, or can be transformed into a two-dimensional information structure on a cosmological horizon, but that, under an alternate description, we literally are information within a two-dimensional information structure on the cosmological horizon - information that can read and interpret itself, therefore, since we can and do read and interpret information. Pixels reading and interpreting pixels!
I think I used the statement "this is not intuitive" earlier in this post.
A few paragraphs ago I said I had a question. Since we, individually and collectively, aren't a Laplace Demon of the waveform and don't have a god's-eye view, should we not question whether we do indeed know how to read and interpret information, since we certainly don't know how to read and interpret all of it? Not that I know if this is a relevant question. This post is not wallowing in relevance anyway. But if we can't read and interpret all information now, how can this global ability exist in a post-black-hole future that conserves our abilities? If a demon doesn't currently exist - if the information doesn't itself create and contain a demon - what right do we have to say that all information has been conserved?
By the principle of conservation of information as I've decided to interpret it, all of my grandmother's information has been preserved and is capable of interpreting itself right now. If indeed this is true, it's not come to my notice.
An answer might be that all information is being conserved, but that it isn't all being interpreted by one centralized overall intelligence, and doesn't need to be. It can affect things piecemeal, this particular thing here affected by that particular bit of information, etc., in the aggregate this resulting in all information being preserved. Presumably all information was being conserved prior to the existence of any intelligence in the universe. An out might be to say that "prior" and "subsequent" have nothing to do with the subject, given reversibility. But then you run into Carroll's questions about whether we do indeed have reversibility. Another out is to say that information need not affect only conscious, intelligent beings: all a piece of information needs is that there be things ("things") that respond to the presence of the piece of information and don't respond (or respond differently) to the absence of the piece of information.
-----
*Nonetheless, here are some relevant Wikipedia links:
http://en.wikipedia.org/wiki/Quantum_state
http://en.wikipedia.org/wiki/Quantum_information
http://en.wikipedia.org/wiki/Physical_information
http://en.wikipedia.org/wiki/Black_hole_information_paradox
http://en.wikipedia.org/wiki/Holographic_principle
Honestly, I've not read through all of these. I need to get this posted, so I can take a nap.
**Laplace, living in the days when Newtonian physics still held sway, believed that if somehow you could know the position and momentum of all particles, you could perfectly reconstruct the past and completely know the future. The imaginary entity that has this vast knowledge, "the future just like the past [being] present before its eyes," has subsequently come to be called Laplace's Demon.
***I don't know if this is right, actually, that "location of the Earth" can make sense as something theory-independent and language-independent. I don't think I need to have an opinion on whether it can, though the concept "location" sure seems comparative, like any form of measurement. AG's distinction seems to be that location is physical (hence will be preserved if physical information is conserved), whereas "1 PM" is conventional (a way of talking about time and location), and while we can choose and change our conventions, we can't change what physical locations are. But my reasoning here is that the location of the Earth is entirely dependent on its relation to something else. Take away Sun and Milky Way etc. and "the location of the Earth" becomes a nonsense phrase. But to make such comparisons, between location of Earth and Sun, and where the Earth is in its rotation, requires brains, even if those brains can apply the comparisons to stars and planets etc. that existed before there were humans. We certainly need theory and language to assign a location to the Earth. And I don't see how we can have any information on the location of the Earth (relative to the Sun or to anything else) without using conventions for talking about location (miles, hours, etc.). Maybe I'm not thinking this through, but the idea of "information" and the idea of "conventions for distinguishing between things and measuring them" seem connected to one another like Siamese twins.
I'll reiterate, a "theory-independent location of the Earth" or "language-independent location of the Earth" is something I don't need to have an opinion on, one way or another, and I don't think anything rides on how anyone "decides" the issue, ever. We'll still need the theories, and language, no matter what. Language-independent locations are something we don't have access to. Language is what creates the access and is what we use to designate a location. So if I had to choose I'd say that "location" is something that doesn't make sense outside of the use of language and of the needs and purposes of language users, the ones who determine location in discourse with one another. "Location" doesn't exist at some "deeper" level. But, as I've also been saying, this question takes us off-topic, and if you disagree with my last two sentences that shouldn't affect our discussion of what is preserved when we say that "information" is preserved. Even if "1:00 PM" is different in kind from "the Earth's location," I don't see how the former can escape being preserved along with all other physical information.
But while I'm here in this footnote gabbing, I'll note that, if we're talking about the location of the Earth, and saying that this is information that is conserved, we mean "location of the Earth" as we currently use the phrase but not as anyone would have used a phrase like it one thousand years ago, when the earth was believed to be fixed and in the center rather than in motion. The heavens were defined as what was above, and the meaning of the term "earth" precluded its being in the heavens. Also note that - as far as I can tell - the holographic principle that supposedly confirms the principle of conservation of information also does a whammy on the idea of "the location of the Earth," which differs depending on whether we're thinking of the 3-D Earth we experience or the Earth as 2-D information on a distant "surface." (Does the holographic principle assume the two "locations" can be translated one to the other as exact equivalents? I'd expect it would, but what I expect isn't based on understanding.)
****As far as I know, the term "mental" plays no role in physics either; our everyday distinction between the "physical" and the "mental" isn't of two states of being, one material and the other immaterial. Presumably, what we call "mental" can be explained physically, though that doesn't mean it has been, yet.
Regarding "information," I suppose someone could talk about "potential information" analogous to how one talks about "potential energy." But for energy to be energy you don't have to call on something from outside of physics, a god's eye or an intelligence or "objectivity." Energy's effects, when it goes from potential to kinetic, are on bodies (or whatever) that are actually part of physics theory. I know quantum physics has something called "virtual particles," a concept I wouldn't dream of pretending to understand. (Wikip: "Virtual particles [just like 'real' particles] are also excitations of the underlying fields, but [unlike 'real' particles] are 'temporary' in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the scattering matrix. As such the accuracy and use of virtual particles in calculations is firmly established, but their 'reality' or existence is a question of philosophy rather than science." That first sentence contains terms that I don't understand, of course.) But for there to be a "virtual intelligence" to be affected by our preserved information, it would have to play an actual role in calculations made by physicists, I'd think. If information has no conceivable effect on anything, how can it be information, or be anything? That's not a rhetorical question, since maybe there's a good answer. I would guess a good answer would be that it does have an effect on something, not that it doesn't need to. But I don't know.
****Sean Carroll may well have said this, or said the exact opposite, in From Eternity To Here, which is a terrific book that I highly recommend but that I understood too poorly to retain much of, especially now that it's back in the library.
There are two main principles in play:
--Quantum determinism means that given a present wave function, its future changes are uniquely determined by the evolution operator.
--Reversibility refers to the fact that the evolution operator has an inverse, meaning that the past wave functions are similarly unique.
The combination of the two means that information must always be preserved.
What I gather from this is that: (i) any present "state" must have a unique past; you can't have two pasts leading to the same present; and (ii) the present can't lead to multiple futures. Am I interpreting this right? So a quantum waveform (?) version of a Laplace Demon** could reconstitute the past or forecast the future (or maybe, this being quanta, could reconstitute past probability wave something-or-other and forecast future probability wave something-or-other) based on what's known now. Hence information is preserved. So, however you twist it, you'll always have the same information.
When people talk about, say, "conservation of energy," I assume they mean that the amount of energy stays the same, no matter what form it takes. Whereas if someone says "conservation of information," I'd think (or guess, anyway) that what is meant isn't just that the amount of information is constant but that any form ("form"?) the information has taken can be reconstructed and whatever form it will take can be foreseen.
(Are reconstructing and foreseeing identical operations? If they're not, I don't understand how information can be said to be conserved. But then, as I say, I don't know what physicists mean by "information," or if they agree about what they mean by "information.")
This is not intuitive, but what's to come is even less so.
Black holes seemed to pose a problem for the principle in that, whatever you put into a black hole, you'd get the same result, a black hole that eventually irradiates away. (Is that the right way to put it, "irradiates away"?) So different pasts produce the same future; the same future can have more than one past. So that particular future doesn't preserve information about its actual, unique past. Currently, Leonard Susskind and crew believe they've definitively resolved the problem in favor of conservation of information, i.e., the preservation of a unique past, the resolution being by way of the holographic principle, though not everyone is convinced. I won't go into any of that yet.
The question I posed last time is, "When physicists say that information is preserved even after everything's been absorbed into black holes that have subsequently evaporated, do they mean that, e.g., 'The test tomorrow is at 1:00 PM' is preserved?" Certainly in my everyday use of the term "information," "the test tomorrow is at 1:00 PM" is information. So I can simplify my question down to this:
Is "The test tomorrow is at 1:00 PM" preserved (by the principle of conservation of information)? If not, what is preserved?
For some reason, I felt ("felt") last time that the answer to the first question was "No, 'the test tomorrow is at 1:00 PM' is not preserved." I had a sense that what the physicists meant was some broader numerical something-or-other about the "state," not specifics such as "The test tomorrow is at 1:00 PM" or "The Sun has eight planets and scads of minor planetoids." Now I'm tending to think ("think"?) the opposite. If physical information is preserved/conserved, this includes, "The test tomorrow is at 1:00 PM."
I continue to have little idea what I'm talking about. But right now I'd reformulate the question as:
If all physical information is preserved, how can "The test tomorrow is at 1:00 PM" not be preserved?
And a corollary to that one would be:
If all physical information is preserved, and this - somehow - does not include "The test tomorrow is at 1:00 PM" being preserved, then how is it possible that "The test tomorrow is at 1:00 PM" exists even now?
So, to convince myself that all information can be preserved while "The test tomorrow is at 1:00 PM" is not preserved, I'd have to have an explanation for why "The test tomorrow is at 1:00 PM" isn't preserved. And to do that, I'd have to have an explanation for how it can exist now without being physical information. We as physical beings sure seem to have the information that the test tomorrow is at 1:00 PM. So far I can't counter this, can't come up with an explanation of how physical beings can have nonphysical information, or what "nonphysical information" would even mean. I don't think physicists, to the extent that they've thought about it, disbelieve that "mental" and "cultural" information can be conveyed by physical information, or that the latter two sorts of information are different in kind from the former. Actually, I don't know what they think. But how would they even potentially explain the existence of "cultural information" at all if such information is not conveyable physically?
That's what I would need to explain, if I wanted to preserve the principle of "conservation of information" while denying the conservation of "The test tomorrow is at 1:00 PM." Not that I necessarily want to deny that "The test tomorrow is at 1:00 PM" can be preserved. What I'm saying is that I don't know how not to preserve it without destroying the principle of conservation of (physical) information - which for all I know is a wrong principle, but to half understand what physicists mean by it, I'm acting as if it's right. Quantum physics guys seem to believe it needs to be right. So, for the moment at least, I'm counting "The test tomorrow is at 1:00 PM" as physical information, hence preservable by "conservation of information."
So, to reiterate, I think the crucial question here, this time in bold, is: How can "The test tomorrow is at 1:00 PM" exist now without being physical information?
I'm deciding for the time being that it can't, and that therefore it is physical information.
In our last episode, arbitrary_greay was playing with contrary ideas, drawing a distinction that I probably don't understand:
Best I can guess is to think in programming terms: at the high-level language stage, variables are given names, and when searching for a piece of data stored in a variable, you call its name, which therefore is dependent on its descriptor. Searching the wrong descriptor will give you the wrong variable, and thus the wrong data.
However, at lower levels, compiler and binary languages, the descriptor is only used as a reference to a location. The data in that location does not change regardless of what descriptor is used to simply "remember" where that location is. I'm guess that "information" is referring to the data (the state of being), not the name given to the location.
AG continues in a later comment,
But the reconstruction of neurons and synapses constructs the words and relations between them in "The test tomorrow is at 1:00 PM," not the location of the earth. The reconstruction of "The test tomorrow is at 1:00 PM" is not necessary to the reconstruction of the location of the earth, which would happen independent of any particular evolution of neurons and synapses. That's what I personally mean when I differentiate being "objects in and of themselves" and being a reference to something else, and why a phrase as a linguistic construct is preserved, but not the phrase as a description of something.
Like in programming: the name given to a variable is itself stored as a series of 1s and 0s (or at the physical level, two different phases of silicon) somewhere on a chip. That is conserved. But when we consider it as a pointer to where some other data is, that data is conserved, and not the pointer.
And that's where we left it.
While I agree that one can know the location of the Earth without knowing that the test tomorrow is at 1:00 PM, I don't agree that, if reconstructing the location of the Earth is the result of conserving all physical information, that reconstructing "The test tomorrow is at 1:00 PM" isn't also the result of conserving all physical information. The mechanism that would give us one piece of information would have to give us the other as well. Or if it doesn't, there has to be an explanation of why not, and I can't think of one.
Even if it's true that the Earth would have had a location without the evolution of neurons,*** this is no more significant than that my grandma would have been born even if later on I hadn't been. That doesn't make me any less reconstructible than her, despite my dependence on her and her independence of me. If conservation of information preserves the location of the Earth, it preserves neurons and synapses, and Russian, and me, and English, and how to use it.
And my second way of putting this is: if all "physical information" can be preserved without preserving English and how to use it, then there can be no good way to explain how physical beings right now have and use English. If a future that preserves all physical information can't figure out what a pointer points at, then neither can we. (This is just a more general way of saying what I said above about "The test tomorrow is at 1:00 PM" being preserved if all physical information is preserved.)
AG seems to be distinguishing between, on the one hand, location and the words that designate it (both the location and the words can have a physical existence) and, on the other, the connection between the words and what they designate, which supposedly doesn't have a physical existence, but rather is set by convention. Whereas I'm arguing that if we, now, physical beings, can connect words and what they designate, then, if all physical information about us is preserved, the connections we make between words and what they designate are also preserved, are also contained within the physical information. Otherwise, how is information informative?
The principle seems either/or to me: either some physical beings can use English, in which case their use of English is preserved along with all other physical information that's preserved by the principle of conservation of information, or not all physical information is preserved/conserved.
[EDIT: When I say "the connections we make between words and what they designate are also preserved, are also contained within the physical information," I don't mean the connections are contained as separate pieces of information, the words and what they designate here, and the connections there. See the comment thread for elaboration (here and here).]
I realize that our experience with fossils and archaeology tends to leave us with bones and markings from which we can at most infer behavior and language, meanings, etc. But then, we don't pretend that paleontology and archaeology give us all the information there is.
But anyway, I'm not yet claiming to understand "conservation of information," what it means. It seems unclear to me as a coherent principle. As Mark says, in brackets (the final statement in the second bracket seeming to contradict all that came before):
[posts above have raised the issue that information in physics terms is not necessarily "communicable" -- as it must be for eg Claude Shannon -- bcz it doesn't require the presence of beings that can "read" the information <--- which is an interesting aspect of the problem, but not one that mathematicians and cosmologists spend much time on; they tend to operate as "under god's eye" communications theorists, even when militant atheists; the information that is an object's waveform structure is deemed "objectively readable" even if no one is EVER going to be around who can actually read it] [for maths and physics this is a side-issue however: information in the social sense is very much NOT conserved, vast amounts is lost everytime someone dies -- the mathematical ideal is that, if the full picture of all waveforms could be retrieved, then ALL information, including the fleeting never-spoken thoughts of the long-dead, could be reconstituted, indeed the retrieval and the reconstitution would kind of be the same activity]
My guess now (as opposed to a couple of months ago) is that the Susskind types would believe that information in the social sense is indeed preserved. They damn well ought to, anyway, because otherwise they ought to contend that information in the social sense doesn't exist now, either.
To think otherwise would put language in a spirit realm beyond the reach of physics, biology, and understanding. Or, anyway would put it somewhere beyond physics and biology. (Are there neo-this-ists and neo-that-ists who believe that reason itself has an existence beyond physics and biology and evolution? And are there people who still believe in Cartesian "mind stuff" (if that's what Descartes believed [I don't remember if I reached that part in my reading of Descartes]? I can't say I'm well read in either old or current philosophy.)
I'm going to guess (without knowing) that Sean Carroll and Leonard Susskind and those types would actually not accept that "an object's waveform structure is... [merely] 'objectively readable' even if no one is EVER going to be around who can actually read it." And I'm kind of hoping, therefore, that they won't accept that social information is lost when someone dies. The dead person's "social" information should be as preserved and reconstructible as any other information. What I'm guessing they would not accept are (1) that it's okay to make your system work by positing a hypothetical but nonexistent entity that "could" read the information, a Laplace Demon of the waveforms or a god or some such (rather, your system needs to function on its own, without adding something imaginary to it; or what you've added must have physical attributes, which you then have to take into account and explain as part of the system, the explanation including how it physically got there); and (2) that the ability to read information is not itself information. In case my double-negative sentence structure is confusing I'll state these in the positive: these quantum physicists should believe that (1) You don't need to assume (and aren't allowed to assume) a god's-eye view or a special Laplace Demon of the waveform because (2) the ability to read the information is information itself and is therefore preserved along with the (rest of) the information. Conversely, if at the end you have to introduce something else, from outside your system, then the information hasn't been conserved. I'll append a (3) which is a variation on (1): "objective" and "subjective" are not terms within quantum physics (you don't talk about "objective quarks" and "subjective quarks," or conduct calculations with the terms "objective" and "subjective"), even if "objective" is a term that some people use to compliment results of quantum physics that they agree with and think are established. So the phrase "objectively readable" has no explanatory power, and can't be called in to make a physical theory work.****
(I do have a question that belongs here, but I won't say it right off.)
So what I'm wanting those quantum physicists to assume (what would seem consistent) is that skills - including the ability to use information, to read it, to understand "The test tomorrow is at 1:00 PM" - are themselves information and are preserved along with all other information. So the information that is preserved includes the aforementioned ability of the information to read and understand itself.*****
Of course, this seems totally absurd, that after every piece of matter is absorbed into black holes that subsequently evaporate, nonetheless we have information left that can read and interpret itself. It's as if we've been made immortal.
But of course, maybe it's equally absurd that we can read and interpret information now, though we most assuredly can. And the fact that we can read and interpret information now is the linchpin of my argument (to the extent I've got an argument).
But I'm not sure (not understanding physics) that the holographic principle doesn't appear equally absurd, in the exact same way as information's ability to read itself appears absurd. And though the holographic principle may turn out to be wrong, it's not being dismissed out of hand by physicists. Of course I don't come within a million and one miles of pretending to understand the holographic principle. What I gather about the holographic principle, though, is that (saith Wikipedia, speculatively) "the entire universe can be seen as a two-dimensional information structure 'painted' on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies." So the holographic principle isn't saying we are represented by a two-dimensional information structure on a two-dimensional cosmological horizon, or can be transformed into a two-dimensional information structure on a cosmological horizon, but that, under an alternate description, we literally are information within a two-dimensional information structure on the cosmological horizon - information that can read and interpret itself, therefore, since we can and do read and interpret information. Pixels reading and interpreting pixels!
I think I used the statement "this is not intuitive" earlier in this post.
A few paragraphs ago I said I had a question. Since we, individually and collectively, aren't a Laplace Demon of the waveform and don't have a god's-eye view, should we not question whether we do indeed know how to read and interpret information, since we certainly don't know how to read and interpret all of it? Not that I know if this is a relevant question. This post is not wallowing in relevance anyway. But if we can't read and interpret all information now, how can this global ability exist in a post-black-hole future that conserves our abilities? If a demon doesn't currently exist - if the information doesn't itself create and contain a demon - what right do we have to say that all information has been conserved?
By the principle of conservation of information as I've decided to interpret it, all of my grandmother's information has been preserved and is capable of interpreting itself right now. If indeed this is true, it's not come to my notice.
An answer might be that all information is being conserved, but that it isn't all being interpreted by one centralized overall intelligence, and doesn't need to be. It can affect things piecemeal, this particular thing here affected by that particular bit of information, etc., in the aggregate this resulting in all information being preserved. Presumably all information was being conserved prior to the existence of any intelligence in the universe. An out might be to say that "prior" and "subsequent" have nothing to do with the subject, given reversibility. But then you run into Carroll's questions about whether we do indeed have reversibility. Another out is to say that information need not affect only conscious, intelligent beings: all a piece of information needs is that there be things ("things") that respond to the presence of the piece of information and don't respond (or respond differently) to the absence of the piece of information.
-----
*Nonetheless, here are some relevant Wikipedia links:
http://en.wikipedia.org/wiki/Quantum_state
http://en.wikipedia.org/wiki/Quantum_information
http://en.wikipedia.org/wiki/Physical_information
http://en.wikipedia.org/wiki/Black_hole_information_paradox
http://en.wikipedia.org/wiki/Holographic_principle
Honestly, I've not read through all of these. I need to get this posted, so I can take a nap.
**Laplace, living in the days when Newtonian physics still held sway, believed that if somehow you could know the position and momentum of all particles, you could perfectly reconstruct the past and completely know the future. The imaginary entity that has this vast knowledge, "the future just like the past [being] present before its eyes," has subsequently come to be called Laplace's Demon.
***I don't know if this is right, actually, that "location of the Earth" can make sense as something theory-independent and language-independent. I don't think I need to have an opinion on whether it can, though the concept "location" sure seems comparative, like any form of measurement. AG's distinction seems to be that location is physical (hence will be preserved if physical information is conserved), whereas "1 PM" is conventional (a way of talking about time and location), and while we can choose and change our conventions, we can't change what physical locations are. But my reasoning here is that the location of the Earth is entirely dependent on its relation to something else. Take away Sun and Milky Way etc. and "the location of the Earth" becomes a nonsense phrase. But to make such comparisons, between location of Earth and Sun, and where the Earth is in its rotation, requires brains, even if those brains can apply the comparisons to stars and planets etc. that existed before there were humans. We certainly need theory and language to assign a location to the Earth. And I don't see how we can have any information on the location of the Earth (relative to the Sun or to anything else) without using conventions for talking about location (miles, hours, etc.). Maybe I'm not thinking this through, but the idea of "information" and the idea of "conventions for distinguishing between things and measuring them" seem connected to one another like Siamese twins.
I'll reiterate, a "theory-independent location of the Earth" or "language-independent location of the Earth" is something I don't need to have an opinion on, one way or another, and I don't think anything rides on how anyone "decides" the issue, ever. We'll still need the theories, and language, no matter what. Language-independent locations are something we don't have access to. Language is what creates the access and is what we use to designate a location. So if I had to choose I'd say that "location" is something that doesn't make sense outside of the use of language and of the needs and purposes of language users, the ones who determine location in discourse with one another. "Location" doesn't exist at some "deeper" level. But, as I've also been saying, this question takes us off-topic, and if you disagree with my last two sentences that shouldn't affect our discussion of what is preserved when we say that "information" is preserved. Even if "1:00 PM" is different in kind from "the Earth's location," I don't see how the former can escape being preserved along with all other physical information.
But while I'm here in this footnote gabbing, I'll note that, if we're talking about the location of the Earth, and saying that this is information that is conserved, we mean "location of the Earth" as we currently use the phrase but not as anyone would have used a phrase like it one thousand years ago, when the earth was believed to be fixed and in the center rather than in motion. The heavens were defined as what was above, and the meaning of the term "earth" precluded its being in the heavens. Also note that - as far as I can tell - the holographic principle that supposedly confirms the principle of conservation of information also does a whammy on the idea of "the location of the Earth," which differs depending on whether we're thinking of the 3-D Earth we experience or the Earth as 2-D information on a distant "surface." (Does the holographic principle assume the two "locations" can be translated one to the other as exact equivalents? I'd expect it would, but what I expect isn't based on understanding.)
****As far as I know, the term "mental" plays no role in physics either; our everyday distinction between the "physical" and the "mental" isn't of two states of being, one material and the other immaterial. Presumably, what we call "mental" can be explained physically, though that doesn't mean it has been, yet.
Regarding "information," I suppose someone could talk about "potential information" analogous to how one talks about "potential energy." But for energy to be energy you don't have to call on something from outside of physics, a god's eye or an intelligence or "objectivity." Energy's effects, when it goes from potential to kinetic, are on bodies (or whatever) that are actually part of physics theory. I know quantum physics has something called "virtual particles," a concept I wouldn't dream of pretending to understand. (Wikip: "Virtual particles [just like 'real' particles] are also excitations of the underlying fields, but [unlike 'real' particles] are 'temporary' in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the scattering matrix. As such the accuracy and use of virtual particles in calculations is firmly established, but their 'reality' or existence is a question of philosophy rather than science." That first sentence contains terms that I don't understand, of course.) But for there to be a "virtual intelligence" to be affected by our preserved information, it would have to play an actual role in calculations made by physicists, I'd think. If information has no conceivable effect on anything, how can it be information, or be anything? That's not a rhetorical question, since maybe there's a good answer. I would guess a good answer would be that it does have an effect on something, not that it doesn't need to. But I don't know.
****Sean Carroll may well have said this, or said the exact opposite, in From Eternity To Here, which is a terrific book that I highly recommend but that I understood too poorly to retain much of, especially now that it's back in the library.