This post will focus mainly on the relationship between four words: information, entropy, order, and chaos. Typically—at least I used to think this way—chaos is thought of as the scientific enemy of life, order, and information. Entropy’s inevitable rise spells death for individuals and doom for our civilizations and information. I picture a world torn apart, a universe of maximum entropy as an endless haze of completely random matter. I now believe that it implies almost exactly the opposite. Well, yes, if your body were fully disordered, you would die. Clearly, infinite entropy does not equate to infinite life. But the truth is closer than you might assume.
I would like to define information as data which could not be predicted.
Useful information is that which you can then use to predict other things (the digits of pi seem to have no pattern and thus contain infinite information, but this information is useful, unlike some other random cobbling together of digits, because they predict many, many ratios with extreme accuracy). This classification is the difference between a textbook and a book full of a random smattering of letters (which may contain more information, despite its uselessness). While this definition of information may not fully agree with yours, it is nevertheless a very useful measure.
Imagine if a company were sending a string of numbers over the internet, and you were employed to make the code used to send this data as short as possible. If the numbers were all “6”s—even several thousand of them—the job would be easy. If it were more complicated, such as thousands of whole numbers in order or the first 500 primes, the code would have to be longer. However, if you had to send 5,000 random digits, your task would be essentially impossible by definition; each digit would imply nothing about the next. One would have to send almost the entire 5,000 digits, with very little compression. Randomness, chaos, and entropy, all imply greater information, not the opposite. Your only chance would be discovering patterns: that, for instance, after every 9th 2 came a 3, or that the 8th digit after every 6 was never the same twice in a row. In merely 5000 digits, some pattern like this is bound to hold, but it does very little to diminish the total amount of information. Thus, information, by this definition, is synonymous with disorder, chaos, and increasing entropy.
Life, too, is built on information and entropy. A perfectly ordered world—a sphere of iron atoms in lattice—would be barren of life. The disorder of our world led to the formation of immensely complex systems. Look at the molecule that stores nearly all of the data representing life on Earth: DNA. It has in immense capacity for information storage; a tablespoon of DNA would be able to hold more data than all of the data stored by all of the computers in the world. This ability stems from its unpredictability: if I tell you there is adenine at spot x in my DNA, you don’t know which base is at spot x+1. Otherwise, one of those bases would be irrelevant. DNA is another example of extremely useful data—it is used to record the traits of nearly all life on Earth.
Essentially, information is disorder, chaos, and entropy. As entropy increases, so too does the total amount of information in the universe. One interesting explanation for this involves quantum mechanics: as time goes on, more and more particles are “observed” to have particular velocities and positions, so our total information increases. Since this data is not predictable from all of the information in the universe before it is known, it is new information, rising steadily along with our entropy. And this rise is not necessarily a bad thing.
A lot of the ideas in this post come from a video I watched a few months ago by Veritasium. I agree with a lot of the video, except for its extrapolations towards the end, which I will address in the next post, I just had to write this one first to clarify some of the ideas in the next.
chris mcelroy 
While chaos is, inevitably, everlasting information, order is also singular information, as pattern.
Like you did, I will use a string of numbers as an example. If sed numbers are in chaos, each number will have no connection to the next, creating an infinite string of information. However, you single this out as the only venue and definition of information. Order is pattern, if you could define it, and within a string of numbers, if you know the pattern, everything else can be predicted. This ability to predict removes the possibility of information within the order, everything that is to come has already came, leaving chaos as the sole provider of information. Although information, at least by dictionaries, is defined as “what is conveyed or represented by a particular arrangement or sequence of things”, and arrange is defined as to “put (things) in a neat, attractive, or required order”. At least in this way, not that I trust provided definitions, information is defined as only order. However, the truth might be somewhere in the middle. As I said, order conveys no information if you know the pattern, but that pattern, made up of chaotic numbers, comes from the order of the sequence. Once you obtain the pattern from the order, it holds no information for you. In order, the only information to be found is the chaotic, ordered pattern, which hold the key to the rest of the, in this case, numerical sequence. In chaos, information still exists, it is just not as singular. In chaos, without pattern, everything holds new information. You could still argue for information as only chaos, however. Order, if it holds information in its own pattern, order’s only information comes from chaos. The only chaos in order is the first iteration of the pattern, with nothing to expect, and this is the only place there is any information to be gleamed. Order and chaos are ringed brothers, chaos in the center, leading to information.
-1n3v1+ab|3
You provide some beautiful imagery here, and more definitions than I did in my own post! I think one problem in your use of the dictionaries (and this probably occurred in my post as well) is the two main meanings of the word ‘order.’ One can either talk about the more verb-like form, “putting things in order” or “ordering items,” or the noun-ish version, such as “the numbers were ordered” or “his desk was orderly.” While these definitions certainly abound in vagueness and ambiguity and such, there are really two main ideas to “order”: the simple fact that things are in a certain list (e.g. the order of the numbers, 3,5,1, and 7), and the idea that the list is reflective of a pattern, or less chaotic than otherwise possible (e.g. the ordered numbers 1,2,3, and 4). I hold that the dictionaries mean more that things happen to be in an order when they say “a particular arrangement.” The dictionary you are quoting is really defining what I called in the post useful information; it is referring to the knowledge conveyed through a particular order, or how useful it is, more than merely how many gigabytes that order might need to be stored. The best example (I don’t know how I didn’t bring this up in my post) is the Library of Babel. It contains every possible 410 page book. Every single one. The interesting consequences of this fill up pages of text; look it up if it piques your interest. To my point, however, this means that each one contains the same amount of information; each book has about 1.3 million characters (in a certain *order*). This doesn’t mean that each book is ordered or instructive at all; most are complete chaos. However, it also holds nearly (assuming some books you read were longer than that) every book you’ve ever read, or every post on this site, in every possible order. It is these books, interestingly, which contain less information than the completely chaotic ones due to the regularities (patterns) in the English language. Those which convey more to us (which your dictionary would call information) have less data stored in them (which was the definition I was using). Neither definition is correct; its just two usages of a word that another language might use to mean pillowcase and pronounce completely differently. In the end, people will hopefully use the definition which is the most useful, which, as you said, is probably the one in the middle; information is only informative if it allows one to learn more information, thus it is never truly chaos.
However, the question of motive still remains. If I had a computer write out a smaller library of Babel, in which each “book” is the length of this comment, it would inevitably print an exact copy of mine. As well as one where all of my errors had been fixed (although that assumes the existence of absolute truth, which I do not, but carrying on…). Does that mean that the computer knows what it is printing? Clearly not, but that does not make the post any less informative? It is just as useful no matter who types it, so I don’t see why not. Essentially, a definition of information as necessarily useful requires an understanding of what use means to the universe. While probably not impossible, it is essentially what Hamlet (and nearly everyone else) struggles with: what makes something useful/meaningful, and why? While I could try to define meaning or use in a relativistic way, they seem to have no absolute definition. Personally, as an atheist with no working definition of life (post probably to come at some point), this is a very hard question to answer on a level that satisfies me, although, on a day to day level, I am able to find enough motivation to make things like this site. I hope this has made you think a little bit, so that my reply satisfies every definition of information I could use (except for pillowcase…).
With each post I become more and more convinced that someone needs to make a Philosopher’s Dictionary, or even another language. Human thought is often hindered by the intricacies of language, I know that it is hard for at least myself not to think with language, but with ideas. However this is exploring a whole other realm of thought, which I will hopefully travel down soon.
Thank you, by the way, for the reply to my earlier post. I know my small reply didn’t cover anything you had said, but your thoughts were less controversial and easier to agree with, so I decided to quickly talk about something else. I continue to be amazed by the level of dedication you put into this site, I come nowhere close to matching the length and thought you put into your ideas.
-1n3v1+ab|3
Yes, language is very interesting; I think I may do my next post on meanings (or lack thereof) of words/ideas. I’m not sure human thought is hindered by it though. I’m not sure I could really communicate thoughts of any real worth to myself (let alone to others) if not through language. Words make thought more rigorous. However, it can be guided and limited by words, especially where availability is low. I was just talking about this problem for running–we only really have 4 words to describe different types of running, but I could easily run about 20 very different ways. Same for nearly every aspect of life: temperature, awesome/beautiful things, pain (how do you describe a headache?), really anything with many types and one main word, or that has a complex and relative scale and not enough words along said scale. In this way, thought is not hindered by language’s intricacies, but by its lack of complexity and detail. This being said, we are already losing vocabulary as it is; would it be feasible to try to teach even more? Especially because most attempts to just artificially add words into english (instead of the “normal” way) don’t seem to work. I’m not that opinionated here, I just find these sorts of thoughts interesting.
Especially because I have to write them in the very language I am critiquing.
Thanks for all of the support by the way–I love knowing that you will comment instead of the silent majority (over 50 now yayyy) who don’t. So thank you and look forward to some great posts in the future, now that I feel like I’ve gotten the main ones I had to do out of the way.
cOOL man. much deep. very philosphical