Any and all information. Information as scientists describe it. I understand that even a Black Hole can’t destroy information. (Suskind, etc)
The reason for my question: Can the information in our minds be destroyed-even after death?
You can see where this is going…
The world is far worse for the destruction of the Library of Alexandria. Yes, information can be destroyed, and sometimes it is far too easy.
As with energy, information (so far as we can tell) can’t be destroyed, but it can be put into an unusable form. While it’s possible, in principle, to recreate a burned book or whatever from the ashes, smoke, radiation, etc., in practice, it’s gone. This is especially so since some of the information will be carried in the radiation that’s traveling away at the speed of light, so there’s no way you’ll ever be able to catch it unless you had your detectors in place in advance.
And black holes are definitely tricky. Everyone presumes that even they can’t destroy information, since the nondestruction of information is such an important foundation for modern physics. But nobody really has anything more than a vague clue about how information could be recovered from a black hole. And, heck, maybe we’re wrong about it being impossible to recover information from a black hole.
Thanks for the response, Chronos. You’ve phrased my question exactly like I wanted it.
But again, just because we cannot access the information, does it exist in some faraway place, like the “End” of Universe or maybe in a different Universe entirely?
I realize there is no definite answer, I guess I’m just looking for opinions, speculations, etc.
I’d like the information in my brain to keep existing Somewhere! 
I do not understand the notion that information cannot be destroyed. I don’t grasp why information would be in any way subject to any kind of law of physics like Conservation of Energy. The information in a unique book ceases to exist if the book is burned. We can only speculate about the information in dinosaur DNA. A binary string ceases to carry information if it is scrambled into random 1’s an 0’s.
Convince me information cannot be destroyed.
Where does a candle flame go when you blow it out?
I think firstly we need a rigourous definition of information to decide if infact burning a book is destroying information (I think you’ll find in the definition in htis context it is not) and secondly information relates directly to entropy and thermodynamics.
My, possibly flawed, understanding of the black hole information paradox is that the number of microstates of what goes into the black hole is not directly related to the microstates of the black hole itself. Information such as, for example, the lepton quantum number of the matter entering the black hole is lost by the ‘no hairs’ theorum. Hawking showed with a neat appeal to semi-classical gravity a mechanism by which black holes can respect the laws of thermodynamics however, Hawking radiation is still only dependent on the state of the black hole and so still cannot account for the lost microstates.
This isn’t about burning books. This is some complicated shit.
That article links to a rather arcane definition of Physical Information:
Unfortunately, it has little to do with information anyone outside the upper echelons of physics would recognize. I don’t think the black hole paradox would have any bearing on the persistence of human consciousness.
Well, “consciousness”, in so far as it can be defined at all, is probably a process, not just a collection of information. There’s a difference between a program just sitting in memory and a program that’s running. But the theoretical physics definition of “information” does encompass the more casual meanings, so yes, the information in one’s brain will in some sense survive one’s death (at least, if it doesn’t end up inside a black hole, about which we’re not sure).
I have seen no evidence that would make human consciousness subject to any law of physics, other than the biologic processes that produce the illusion of sentience.
What makes the book actually represent information? What is the definition of information?
With respect to the book that was burned it represented information only within the context of someone that understood the book. For someone from a different planet that just happened to use the exact same letters as we do, the entire book could simply be that person’s name.
Which representation of information is correct? Is information lost when the book moves from our planet where is contains lots of stuff and ends up on another planet where it only contains 1 person’s name?
If the quantity of information is completely dependent on context then the term “information” really applies to the mapping from a specific source to a specific consumer, as opposed to some underlying foundation, which seems completely relative and not very useful, which means maybe the physical approach makes some sense. Not sure, just thinking out loud.
I would define information as the mapping from a one consciousness to another. Whether that is useful in physics is really not germane. Without consciousness, information is meaningless. It is unfortunate that the same word means two very different things to different disciplines.
There seems to be some confusion about what “Information cannot be destroyed” means. Well, I don’t know how a physicist uses the terms, but here’s my guess: to the weakest possible first approximation, the claim “information cannot be destroyed” at least implies “Physical laws are such that it is possible in principle to determine the entire state of the universe at time T1 from a description of the entire state of the universe at time T2, so long as T1 is prior to T2”; i.e., “Physical laws allow us to deterministically rewind a description of the universe” (as otherwise, information about the prior history of the universe is lost over time).
“Information cannot be destroyed” may be meant in an even stronger sense than this (e.g., perhaps something like, “Even given some uncertainty in one’s knowledge of the state of the universe at time T2, the corresponding uncertainty in one’s knowledge about the state of the universe at earlier time T1 can be no greater (for some particular measure of ‘uncertainty’, a la entropy)”), but I think that qualitative starting consequence is easiest to grasp.
So how would you respond to my book example that is being interpreted by two different people on two different planets with different context?
It is still information. A book is still information even if someone is illiterate. At some point, they can learn to read, and the information is transmitted.
This my understanding:
A macrostate is the observed state of the system. Generally speaking our knowledge of a physical system is not perfect and the macrostate will actually correspond to a ‘number’ (scare quotes as more often than not we’re dealing with continuous variables) of different allowable states of the system. These exact states are called microstates of the macrostate. Loosely speaking the ‘number’ of microstates corresponding to a macrostate corresponds to the entropy of the macrostate. The more microstates in a macrostate, the higher the entropy. In quantum mechanics the macrostate corresponds to a mixed state and a microstate corresponds to a pure state (i.e. we’re talking about imperfect knowledge of the sysetm as opposed to quantum uncertainty)
If the time evolution of several microstates of an isolated system is degenerate then that clearly presents a problem as it suggests that the entropy of the system will spontaneously decrease flying in the face of the laws of thermodynamics.
I think there is a need to distinguish between information in the (rather technical) sense in which it is used in physics (and mathematical information theory), and meaningful information, of the sort that you might find in a book or a radio signal, or whatever: information that can potentially be understood by human beings. The latter is really the everyday, colloquial sense of the word. The former gets to be called by the same term because physical information can be (and sometimes is, but often is not) used to carry a meaningful message, and, indeed, meaningful messages cannot be conveyed except via physical information. Information in the physical/information theoretic sense is more like the potential that a certain physical system has for conveying meaningful information, and although this potential cannot be destroyed, any particular meaningful information that a system carries can most certainly be destroyed (as when a book is burned) when the physical information is converted into another form.
You could, for instance, take the ashes of a burned book and arrange them to spell out some sort of message. Thus the potential for conveying meaningful information is still there in the physical system. But that is to create new meaningful information, not to preserve what was originally there in the book. (We still don’t really understand how meaning is created by people, but it clearly happens all the time.) On the other hand, nobody might bother to re-arrange the ashes into a message, and the ashes, as they come from from the fire, mean very little except “something has been burned here,” which (although we cannot quantify meaningfulness more than very roughly) is certainly far less than was in the original book. In this case, meaningful information has been destroyed, even though physical information (or the potential to carry meaning) has not.
Another, perhaps better example of the distinction occurs to me. Take a book - War and Peace, for instance - and reprint a version of it with all the letters, spaces, punctuation marks etc., scrambled in random order, so that the new version contains exactly the same number of e’s, w’s, b’s commas, spaces etc. as the original work. The new version embodies just as much physical/information theoretic information as did the original version, but it conveys no meaning whatsoever. Again, meaningful information has been destroyed, even though physical information (and the potential to carry meaning) has not.
If you are concerned with consciousness, you are really concerned with meaningful information, not (primarily) the physical sort.
According to Zen and the ART of Motorcycle Maintenance a motorcycle is pure information. Even the raw materials in a sense are just specified information.
On the other hand lets say I’ve never read War and Peace (actually I needn’t be hypotehical here as I haven’t), I do know however that it has to make sense in English (which I do know), assuming of course we’re talking about the English translation. The fact that it has to make sense in English severely constrains the possible order of the letters/symbols. This is infact a crude example of macrostates vs microstates.
Using that definition, all matter and energy is information, because it has the potential to carry information. There is no distinction betweeen information and non-information beyond that which exists, and that which does not exist. That broad interpretation may be useful in physics, but has little utility elsewhere. It is confusing when physicists appropriate a term with a vastly different meaning to the lay person.