How does science define information?
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)
Is everything information?
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."
And can information exist without a consciousness to perceive it?
Sure. Every motion detector security light acts on its received information just fine without any conscious involvement.
Is misinformation information?
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.
If information is indestructible, where is it when it is no longer present?
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.
If you burn a book, have you not destroyed information?
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.
