Information Paradoxes

Information is a curious thing. In fact, it’s several curious things: firstly, it’s concepts, secondly, it’s words and pictures, and thirdly, it’s very paradoxical. Basically, information is the blanket term we use for things that have content that can be moved. An explanation of these terms would take literally forever. Go and look it up. I’m not your mother.

The problem is that information is a fiendish beast. Philosophers, mathematicians and scientists are more or less in agreement on one thing: paradoxes don’t happen in the real world. Unfortunately when it comes to information they certainly seem to. A famous science example is the Einstein-Podolsky-Rosen paradox, where if you take a pair of particles that match and send them to the far ends of the universe, and then change one of them, the other will change instantly. Somehow information is passing between them faster than the speed of light (which can’t be done). Boosh. Paradox. Which is terrible, because in this case information relates directly to the world we live in.
Sort of like this Dilbert cartoon, which is vaguely related to the topic.

Sort of like this Dilbert cartoon, which is vaguely related to the topic.

Less esoteric example of information paradoxes exist. A short story follows…
I briefly worked for a large company in the Spanish capital, Madrid. Across the road was a building with a sign outside called Sapphire. Every morning, while smoking a cigarette, I would look at this sign and try and work out what the company was. Shops and businesses in Spain are fairly explicit when it comes to explaining what they’re selling; for example, grocery shops are called Alimentacion (literally, “nourishment”) because they sell food, and shops that sell sheep heads and those little packets of instant noodles are called Alimentacion Internacional. Shops where you buy telephones are called Telefonica. Shops owned by Chinese immigrants are literally called Chinos (which I’m sure is derogatory). Hotels are all called “hotel something-something”, in contrast to the UK where brand names like Hilton, Astoria and Travelodge stand in for a descriptive. You get the idea. Nuance is not a key feature, which is why I had such trouble with Sapphire.
It took me a long time to realize that Sapphire was a gentleman’s club where women take their clothes off for money. This realization was prompted by the hypothesis that, if every shop is keen to tell you what it sells, the only shops lacking descriptions would be those that didn’t want everybody knowing what they were selling. In an ostensibly Catholic country, titty-bars and brothels are the only shops that don’t proclaim their wares.
Come on, I literally HAD to use this picture at this point. Don't judge me.

Come on, I literally HAD to use this picture at this point. Don’t judge me.

This got me thinking about information paradoxes. You see, information is a way of taking concepts from person A and putting them into the head of person B. Language is all information, for example. Shop frontage is another. Words, pictures and concepts are all information by dint of having content: a rose is a rose is a rose, as Gertrude Stein would have it (or, as Ernest Hemingway infamously posited, “a bitch is a bitch is a bitch”, which was probably unfair on Stein). “Roses” are concepts and things and words that contain content. Yet, in my lame story, you have a paradox, because in that case the absence of information was itself information.
I’ve never come across this paradox before, so I might claim it as my own (“q.v. Rayneau’s Paradox” might yet appear in the Britannica) but it clearly illustrates how tricky information is to get a grip on. There is a more obvious hypothetical example: you go to a shop and try on a new blouse/shirt/skirt/gimp costume and you think it looks pretty neat. You buy it and take it home, put it on and show it off to your wife/husband/boyfriend/hamster. And they say nothing.
They absence of information is informative in this case because, paradoxically, it conveys information. Your significant other might be dead/blind/sulking/on fire/a hamster. More importantly, the lack of a response usually tells us that something is amiss. If you’ve ever been in the situation where you were sent out to buy milk and returned with a gimp suit, you know I’m right when I say that an argument is brewing.
Hilary Putnam once phrased this in his famous Twin-Earth hypothetical. I went over this too many times in University to want to write it out again, so here’s a crib:
“We begin by supposing that elsewhere in the universe there is a planet exactly like Earth in virtually all respects, which we refer to as ‘Twin Earth’. (We should also suppose that the relevant surroundings [are exactly the same as for] Earth; it revolves around a star that appears to be exactly like our sun, and so on.) On Twin Earth, there is a Twin equivalent of every person and thing here on Earth. The one difference between the two planets is that there is no water on Twin Earth. In its place there is a liquid that is superficially identical, but is chemically different, being composed not of H2O, but rather of some more complicated formula which we abbreviate as ‘XYZ’. The Twin Earthlings who refer to their language as ‘English’ call XYZ ‘water’. Finally, we set the date of our thought experiment to be several centuries ago, when the residents of Earth and Twin Earth would have no means of knowing that the liquids they called ‘water’ were H2O and XYZ respectively. The experience of people on Earth with water, and that of those on Twin Earth with XYZ would be identical.

Now the question arises: when an Earthling (or Oscar for simplicity sake) and his twin on Twin Earth say ‘water’ do they mean the same thing? (The twin is also called ‘Oscar’ on his own planet, of course. Indeed, the inhabitants of that planet call their own planet ‘Earth’. For convenience, we refer to this putative planet as ‘Twin Earth’, and extend this naming convention to the objects and people that inhabit it, in this case referring to Oscar’s twin as Twin-Oscar, and Twin-Earth water as water.) Ex hypothesi, their brains are molecule-for-molecule identical. Yet, at least according to Putnam, when Oscar says ‘water’, the term refers to H2O, whereas when Twin Oscar says ‘water’ it refers to XYZ. The result of this is that the contents of a person’s brain are not sufficient to determine the reference of terms they use, as one must also examine the causal history that led to this individual acquiring the term. (Oscar, for instance, learned the word ‘water’ in a world filled with H2O, whereas Twin Oscar learned ‘water’ in a world filled with XYZ.)”

Putnam concludes by saying “meanings aren’t in the head”. This is a tricky problem in Philosophy, not because it means anything (it doesn’t, it’s garbage and it represents four wasted years of my life) but because it’s a pretty watertight argument for an idea that doesn’t make sense and doesn’t mean anything.
If you’re trying to figure out an alternative solution, don’t bother: there isn’t one. The only way to solve Putnam’s Twin Earth problem is to scrap the hypothetical situation and work from there. In actual fact, for those of you doing the Phil914 course there is a quick solution: meanings aren’t truly shared. Words, shapes, pictures etc are sort of banknotes that are exchanged between banks. In this case the banks are our brains and they work at different conversion rates. The solution follows neatly from there: Oscar, when he thinks of “water”, thinks of rolling waves. Twin Oscar, on the other hand, thinks of babbling brooks. The concepts are different, the words are the same. Therefore, it doesn’t matter what they mean (water or XYZ), just that they’re on the same page concept-wise. SUCK IT, PUTNAM.
Better informational paradoxes exist. A less famous but equally-significant one is called Arrow’s Information Paradox, which briefly states that when it comes to intellectual property, a seller will often give the product away for no compensation. I call it the “Why I Don’t Buy DVDs of Films I’ve Already Seen” argument.
A good example exists in the “Teach A Man To Fish” cliche. The paradox lies in the fact that can teach somebody, but you can’t sell the idea of fishing to somebody who doesn’t know what fishing is without basically explaining what fishing is. For example:
A: “If you give me some money, I’ll teach you fishing.”
B: “What’s fishing?”
A “It’s a way of catching fish.”
B: “I’m still confused.”
A: ” Basically you use nets or a baited line and pull the fish out of the water.”
B: “Oh! Actually, I think I got this.”
A: “God damn it, there goes my commission.”
Arrow’s Information Paradox is basically like selling doors, door-to-door.
To get back to the DVD problem I mentioned: you know that little warning that comes up before the movie saying, “please don’t record this movie, it’s not very nice and we might have to break your legs if you keep doing it.” Unfortunately everybody in the theatre is ignoring that warning by having working eyes and a memory. Information (to whit, intellectual property) is being recorded by the most sophisticated camera known to man: the human eye. Sure, it’s not perfect, the DOLBY surround is missing and there are gaps when you went to the toilet, but basically information has passed from place to place, violating copyright laws. Buying the DVD is just adding insult to injury. And adding to the global plastic crisis. The same thing happens with songs: how many times have you sung a song you don’t own on CD? Technically, if it exists in your head, it’s information. It’s an MP3. And you’ve broken copyright.
Sort of like I did with the Dilbert cartoon. XKCD will make up for it.

Sort of like I did with the Dilbert cartoon. XKCD will make up for it.

The point I was trying to get across is that information is a very tricky thing to understand. Sometimes it’s there,sometimes it’s not but isn’t, and sometimes it copies itself. All of this is dumb speculation until you consider this: we live in a world governed by information. It controls our lives. Our bank balances, social security deposits and personal details are all information now, moving here and there and obeying their own, strange laws. Some are worried that the NSA and GCHQ will use this information to control our lives. Others think it heralds an era of unparalleled openness. Really, though, we should be making these kinds of leaps after we’ve figured out what information is.
In fact, I was going to make that point, but then I thought about something my father does. He’s got into the habit of watching movie trailers on TV and at the end of them saying, “well, I think I saw the best bits, I don’t need to buy a ticket”. My father is living proof of Arrow’s Information Paradox. Bravo, dad.

3 responses to “Information Paradoxes

  1. Nice write up mate, liked Putman’s idea, true that everyone’s just another version of reality; eg violence is a fear for some and a love for others depending on how you learned it

  2. Hi. Nice blog. Now that you put it this way, I realised that I’ve been using lack of information to arrive to my conclusions. I remember asking someone if he loved his wife, and there was a pause, longer than usual. Whatever he said after the pause didn’t count anymore, because the pause told me more..

  3. Pingback: Using the R Word | James Rayneau·

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