How does science define information? Is everything information? And can information exist without a consciousness to perceive it? Is misinformation information? If information is indestructible, where is it when it is no longer present? If you burn a book, have you not destroyed information?
It depends upon the specific field of study or work. There is arguably no overarching agreement. Even something that seems as broad and basic as "a pattern that causes a repeatable effect in what receives it" could encounter conflict with what the term rigidly and narrowly signifies in the nomenclature of some obscure research enterprise. - - - - - - - - - - - Rafael Capurro: Almost every scientific discipline today uses the concept of information within its own context and with regard to specific phenomena. Can a common meaning for this term be derived, or do we have to agree with the skeptical view expressed by Bogdan?[1] My skepticism about a definitive analysis of information acknowledges the infamous versatility of information. The notion of information has been taken to characterize a measure of physical organization (or decrease in entropy), a pattern of communication between source and receiver, a form of control and feedback, the probability of a message being transmitted over a communication channel, the content of a cognitive state, the meaning of a linguistic form, or the reduction of an uncertainty. These concepts of information are defined in various theories such as physics, thermodynamics, communication theory, cybernetics, statistical information theory, psychology, inductive logic, and so on. There seems to be no unique idea of information upon which these various concepts converge and hence no proprietary theory of information.[2] A broad philosophical debate continues as to whether the concept should address a knowledge process including, as a necessary condition, a human knower or, at the very least, an interpretative system, or whether it should exclude mental states and user-related intentions and be considered as addressing an objective magnitude or property of beings. Between these two positions are different kinds of mediating theories, including the quest for a unified theory of information. This controversy reflects the complex history of the term. --page 356, "Information As An Interdisciplinary Concept" ... THE CONCEPT OF INFORMATION (2020) - - - footnotes - - - [1] Bogdan, R.J. (1994). page 53. "Grounds for cognition. How goal-guided behavior shapes the mind." Hillsdale, NJ: Lawrence Earlbaum. [2] Actually, Bodgan himself develops a general view of information that stands in contrast to this skeptical quotation. _
There's no consensus, as C C said. Reading through the previous post, I like the idea that information is something that can be transmitted as a message over a communications network of some kind. There are different ways we might go about measuring the "information content" of any particular message. Oh God, no. Don't start that in yet another thread! That's practically an invitation for Write4U to appear and start talking about "mathematical values". My answer is: no; obviously no. You can't, for instance, send a banana down a phone line. Debateable. It depends on how you define it. It can certainly be sent down a phone line. Or across a broadband connection. Again, I think it depends on your definition of information. Intuitively, it makes sense to me that if you burn a book you could be destroying information. But it is also possible that the same information could be found elsewhere.
Scientifically, information is any unexpected bit of data. You stumble on a set of data and the first five elements are 1,2,3,4,5. You anticipate a pattern, and guess that the next number will probably be 6. If it is, then you have learned very little you didn't already expect from the first five. The information value of that 6 is low (though it is not zero). You stumble on a set of data and the first five elements are 12, 1, 47, 1.5, -93. You likely won't be able to guess the next number. The next element will be information of high value. This is how many forms of file compression work. If a sequence in a file goes from 1 to 100 (or, even better, a string of 100 zeros) it is predictable enough that we don't need to record every digit. There are much shorter ways of saying "and then 100 zeros" because there is not very much information in there. In short, information is the arrival of the unexpected. Shannon entropy: "The core idea of information theory is that the "informational value" of a communicated message depends on the degree to which the content of the message is surprising. If a highly likely event occurs, the message carries very little information. On the other hand, if a highly unlikely event occurs, the message is much more informative. For instance, the knowledge that some particular number will not be the winning number of a lottery provides very little information, because any particular chosen number will almost certainly not win. However, knowledge that a particular number will win a lottery has high informational value because it communicates the outcome of a very low probability event." https://en.wikipedia.org/wiki/Entropy_(information_theory) Ehhh. Everything has degrees of information. A uniform straight line segment tells you something at first, but less and less the longer it gets. It never reaches zero, baceuse even if it is ten miles long, it's telling you "I am straight for at least ten miles." Sure. Every motion detector security light acts on its received information just fine without any conscious involvement. Yes. it doesn't have to be true to be information. But again, this is a in a pretty rigorous application of the word. It is a word with so many meanings, highly dependent on context, that it is very easy to abuse. One must specify the specific use one intends when using this word. Look up "weasel words". Information, as a word is very fraught with the pitfalls of weasel words by the unscrupulous or the merely inexperienced. The definition of "information as truth" is only one form of the word. That's why I led off with "scientifically..." And even that is very broad. Information theory is a discipline unto its own. Just like a chemistry set, you don't want to just start mixing stuff randomly without expecting something to go boom. Where are numbers when they are not in front of you? More helpfully, information isn't so much a thing that exists here or there; it is more like an event, a process - an arrival of data at a receiver. Ehhh. Books have duplicates. The book itself is not the information. The idea behind the indestructibility of information is more like this: even if you burned the book, the gases and byproducts are still a direct deterministic outcome of the initial state of the book. The paper, the ink and the shapes that the ink formed on the pages have certainly been thoroughly randomized down to a molecular level, but that's not the same as destroying it. In principle, with sufficient perceptual and mechanical acuity, those gases and byproducts could have their trajectories reversed until the book is recreated. Like smashing a glass of milk on the floor and reassembling it back into its original form. The information of the glass and milk and book has not been destroyed. It's still there - if practically inaccessible. In contrast, they say that a black hole does destroy information. If you waited for a black hole to evaporate, and collected all the products that offgassed from it, you would not be able to reassemble that matter into its original states (of stars or planets or whatever). The initial state of matter that falls into a black hole is not retained - it is truly destroyed forever. This has been a primer of what infrmation generally means in a rigorously scientific and mathemtical context. It's not really the common use of the word in our society, which is much more involved with truthfulness.
Applying the definition posted above, would the set of all prime numbers be an infinitely informational set? Is the universe infinitely informational?
The primes are predictable and calculable. In the strict sense of information-as-surprise, the primes are not new information. But again, I strongly caution that this is pretty strict definition of the word in a pretty specific context. A cheat sheet that contains the first thousand primes for easy reference is pretty useful information for the college math student. As you can see, there is a diminishing benefit from these answers to questions about information in its generic sense. Every comment made here in this thread has an exception in other flavours of the word. At some point, you'll have to specify what you mean by information to get any meaningful answers.
Like any term, it depends on how you use it. As I understand it, in quantum physics, much like energy, information can be neither created nor destroyed since in quantum physics there is no distinction between running time forward or backward. Obviously, if you burn a book you've destroyed the information in that book. If you can run time backward, you have not.
Reversing time is one way of supposing one can retrieve the information, but it doesn't have to literally require reversing time. In principle at least one can take the current state of every particle and extrapolate back to its inital state. A burned book certainly has all its information randomized down to a molecular level, but the information is not strictly considered lost. Every atom and in the burned book owes its current position and momentum to where it came from (and the energy involved). That means its initial state is still encoded in its present state. The information is obfuscated, but it is not considered - in information theory - destroyed. It's kind of splitting hairs - just pointing out that reversing time is not strictly necessary.
