The Stripy Strudel's Journal

In an imaginary, ideal and pitch abstract world live people who don't give a damn about being trapped in our thought experiment: they're people, too, and try to get their human fun from life. Just like us, they meet, make friends, mix and give each other simple pleasures. And just like in our world, they have social obstacles, having grown up in somewhat different cultures and then gotten mixed together. That's why what's natural for some is unthinkable for others.

For example, some people love massage of the head so much that they're willing to spend hours scratching, stroking and massaging each other's heads — if they find someone like them. But here's the catch: for some others touching the scalp is a taboo that can't even be mentioned. Because nobody knows whether it's disgusting or delightful for someone, you can't really offer this to a person: what if they get offended? So two head massage lovers don't dare to offer it to each other because each one of them is afraid that it's unacceptable for the other. Same thing with nose-rubbing, round dances, riding horses together, pat-a-cake and numerous other ways in which our speculative poor things bring enjoyment to each other.

Here is the problem the society is facing: invent a way for fans of various pleasure to recognize each other. It seems trivial: why not introduce conventional signs? For example, a red T-shirt could mean a round dance devotee. But it's not that easy: a round dance lover wouldn't like those for whom round dances are a taboo to know about their devotion. Hey, there are places where they won't let you in if you wear that! Therefore, a signaling system has to be more selective.

Let us call the whole range of ways to please each other acceptable for a person their easiness, as in “he's an easy (uncomplicated) person”, “she's easy to be with”. An easiness is a mathematical set. Let us designate the easiness of a person X as E_X. Then the requirement to a signaling system should be stated as follows: for every person Y, conventional signs worn by Y should suffice for X to derive E_X ∩ E_Y. Consequently, for each of his devotions X will only find out whether it's shared by Y, but he won't find out about those of Y's passions that X himself dislikes. He'll find out what he can what he shouldn't try with Y, but won't know anything shocking or destructive to their friendship.

A solution to this problem can be a variety of signs with limited knowledge of them. For every questionable pastime A enthusiasts establish a club, society or some other kind of community for A-doers. To become a member, one needs to do A with any current member. For lovers of A it's not a problem but rather a pleasure, but those for whom A is unacceptable won't even think about joining the community. Of course, the lists of community members are kept in secret. Because the world is ideal, everyone knows about every such community, and can and will join all the relevant ones. In a closed meeting, members of the A-doers society decide on a sign by which fans of A will recognize each other. It can be anything: an item of clothing, an accessory, a feature of speech or gait, a code word or gesture. Different communities pick essentially different signs, so that it's impossible to tell by the look of how many communities a person is a member. This way, everybody only knows the signs of belonging to those communities one is oneself a member of, and when X and Y meet, they instantly see what their common easiness, the intersection of E_X and E_Y, is, and within that intersection they feel at ease with each other.

The problem and the solution have been found in brainstorming together with Wheezle, for which I'm thankful to her. This way, we have determined by experiment that joint brainstorming is included in our common easiness. And if you, my dear readers, also love head massage — welcome to the club!

По-русски: Общество любителей фантазировать с умным видом

Note: This has been initially posted as a comment in a discussion about a recent epidemic of a social virus about a little girl needing blood for transfusion. The fake message has been started by a LiveJournal user, and contained a plea to forward it to as many people as possible.

During the recent epidemic, I've got the message saying that someone needs B group blood dozens of times, and the shocking thing about it was that some of the people I got it from were:

1. Smart people, and I've got no doubt about it. I can warrant that some of the people whom I got the message from are smart, I've been studying together with them and I know them rather well. They are capable of complex mental activity both at work and in private life (so that it's not “common idiocy” when a professional outside of his workplace is helpless and naïve like a child).
2. People we haven't talked with for quite a while. If those people decided to send the message to me, it means they were sending it to everyone in the contact list, and maybe even outside the contact list.

The most scaring is that the first and the second groups have non-empty intersection.

A little analysis.

None of the forwarders tried to change the text or at least add something to it like “Do you think it's true? What if it is?” to express their degree of trust for this information. Does it mean everyone trusted it for 100%? Of course not. Maybe the hoax got them convinced for 60%, and they decided to forward it. But forwarding or not forwarding is discrete, it's either 0 or 100%. This way, 60% is rounded up to 100%, so we end up with stable reproduction of the worm. If every forwarder expressed their degree of trust, after three or four hops the information would “fade out” and turn into a tale that nobody is going to believe. It's this “rounding” that ensures the reproduction of the worm: the forwarded message looks exactly the same as the original. No gossip transferred the traditional way, through mouth and ears, achieves such steady reproduction as an electronic rumor gets nowadays when text can be copied and forwarded without distortion (experiments show that oral rumors, even when the forwarders are actively trying to reproduce the information exactly, get distorted to full loss of content after ten hops, and after three or four they loose half of the meaningful content).

Why does spam about this subject get reproduced the most steadily? One could build a mathematical model of gossip reproduction with the following parameters:

1. Persuasion threshold — the degree of belief necessary for the reader to take the information seriously.
2. Eloquence coefficient — the factor (usually less than one, but may as well be greater) expressing how the persuasiveness of the message changes when it's forwarded once. For electronic messages forwarded by verbatim copying, the factor equals to one.
3. Distribution factor — the number of recipients that a single participant decides to forward the information to when 100% convinced.
4. Connectedness characteristic — a property of the acquaintance graph (the average number of common contacts that two people in contact have).

Because the connectedness characteristic is a property of the medium and doesn't depend on the message content, this leaves us with the remaining three values. All of them affect the process of message distribution. When the persuasion threshold is high, the eloquence factor is low, or the distribution factor is low, the process fades out after some predictable number of links. This is what happens to most of the lucky mails: you usually get them from a contact or two, but no real epidemic begins. However, when the aggregate attenuation factor (the ratio of the number of active forwarders on the current iteration to that number on the previous iteration) that depends on the aforementioned parameters is greater or equal to one, the process doesn't fade out but instead continues until all closely-linked part of the acquaintance graph is informed. In practice, that means informing close to all potential forwarders in the Russian part of the Internet.

The persuasion threshold, the eloquence factor and the distribution factor depend on the message content. What made the aggregate attenuation factor exceed one in this case? The persuasion threshold, as it seems, is lowered for messages of this type because people prefer to be safe than sorry: “I'm only 25% convinced that it's true, but if it is, I could save someone's life by forwarding this”. However, the potential forwarders in LiveJournal are gullible enough already, one just has to remember this: “They're going to make ICQ a paid service. To not let it happen, please forward this to all your friends”. So I don't think it was the persuasion threshold that played the crucial role. The eloquence factor of one is also typical for electronic communication (though in some cases the forwarders decide to retell the message in their own words, which usually makes the eloquence factor less than one). This leaves us with the distribution factor. An indirect confirmation to this is that I received the message from some people I rarely talk to. It's for this specific kind of information that the distributors feel it especially important to maximize the number of recipients by all means because they think that someone's life depends on it. (The latter might not be exactly true. For the most, as it seems to me, it's more important to ease their own conscience than to save the little girl's life, and to ease the conscience, one has to perform the ritual of forwarding the message to everyone possible, so that one can say: “I did for the unfortunate wretch everything I could”.)

По-русски: Факторы воспроизводства социальных вирусов

When a programmer has nothing better to do, or he just needs an exercise for the brain, he starts having these weird ideas. Like Esoteric programming languages.

All our boring programs are grossly one-dimensional. The memory is linear, the stack is sequential, the program is transcribed in a serialized form. Even things that are naturally two-dimensional, such as the on-screen picture, are reduced to linear for computer processing. The idea of taking programming beyond the one-dimensional space isn't new and has already generated a whole family of esoteric programming languages called fungeoids after the first of the kind, Befunge. The common feature of these languages is transcription of the program as a two-dimensional matrix containing the operation codes. The interpreter moves proceeds from one cell to another in one of the several possible directions. This way, a loop in Befunge can indeed have a loopy look. Some of these languages use memory registers isolated from the program storage space and are addressed by one-dimensional indices; others use the Von Neumann architecture and store data in the same two-dimensional memory as the code, which also creates interesting possibilities for writing self-modifying programs.

The reader might ask why anyone would need any of it, whether someone indeed has nothing better to do, and what kind of mild drugs the author uses, so I'll have to answer. No particular reason. Simply put, it's for fun. Hey, ask some solid scientists specializing in pure mathematics why they have to study objects like… well, not just an algebra, and not even en algebra of algebræ, but an nth order algebra, an algebra of algebræ of algrebræ… n times. I suppose their elaborate answers can be effectively reduced to something like: “Hey, it's fun!” So is an esoteric programming language fun. It's an original joke, and a complicated mathematical abstraction to study, and a puzzle. Taking something to the point of absurdity is fun in itself, so today I've taken it to my hand to carry the idea of multidimensional programming to absurdity. Let's do it in three nonsensical steps. I'll be writing about the two-dimensional case, but it's trivial (?) to generalize for the case of n dimensions.

First level. Here lie the “arrow programming” languages of the fungeoid family. The memory is two-dimensional. In a more interesting variation, the memory is shared between code and data. On this level, each memory cell stores an ordinary number, such as one byte. Let's call the data unit stored in one cell a word, as in traditional computing. Two-dimensional memory uses two-dimensional addresses, such as (i, j). The current instruction pointer (IP) also looks like this. Most fungeoids allow to change the direction in which IP is incremented to one of the four ways, but it's not necessary for Turing completeness: a single direction and a conditional jump to a two-dimensional address is enough. However, the changeable direction of execution flow is the fungeoids' zest which makes programming in them especially unlike the traditional and allows transcribing of loops as rings and linear programs as spirals. Two-dimensional memory organization inspires thoughts of measurement units such as square kilobytes (Kb²), makes you think about what the operating system should do when it gets a request to allocate a wide memory block while only tall and narrow areas are available, and gives rise to an interesting problem of defragmentation of rectangular files in two-dimensional mass storage. The compiler could optimize code not only for speed but also for the area taken, and storage of raster images would be natural as never before. Finally, programming languages can be described by two-dimensional grammars specified in BNF².

Second level. Unlike the first level represented by numerous fungeoids, I've never encountered anything that would fit my second or third level. In the second level, something strange happens to the very numbers: they are not simple bytes anymore but rather complex values. Addressing a cell of the two-dimensional memory becomes natural. Addition and subtraction are straightforward, multiplication and division are slightly more complicated, and there is a new operation: complex conjugation. One could even go further and say that the cells contain two-dimensional matrices of bits. For example, a word can be comprised of 16 square bits (4×4), which, of course, spawns a new set of arithmetical operations. With regular addition, the overflow bits are carried in one direction — to the left; with two-dimensional addition, bits can be carried both to the left and up. This makes at least two types of addition and subtraction. Shifts and rotations can be done in four instead of two directions, and new operations are possible, such as turns and transposition. When multiplying, shifts are made in both directions. It's not obvious, though, how a two-dimensional word should be interpreted as a regular number for purposes of addressing and counting. Speaking of data exchange in networks, instead of two possible bit orders (little-endian or big-endian) we get eight equally reasonable ways to serialize a word.

Third level. At the third level of absurdity, time becomes two-dimensional. Who cares that it doesn't apply to our Universe? The model is interesting anyway. A moment of time is described with two variables (t, u) rather than one. With regard to a single moment, there isn't just something that happens before or after; there are some moments to the right from this moment in time, some below, and some both to the right and below. The causality spreads in both directions, and what happens in a moment of time is a consequence of both what happened to the left and above in time. Clock frequency is measured in square Hertz, and the state of the machine at clock (t, u) is derived from its states at clocks (t – 1, u) and (t, u – 1). The program stored in the two-dimensional memory runs both horizontally and vertically. In the next clock by t the CPU proceeds to the command to the right of the current, and in the next clock by u it moves to the command below. A bicyclic algorithm can have toroidal topology. In a square second, a communication channel can be used to transfer a number of square bits, therefore the throughput is measured traditionally, in bits per second. The task of optimizing the speed of an algorithm can be defined more accurately: which of the time dimensions is more important to optimize.

Fourth level. If someone comes up with a fourth level to complement the three above, I'd like to discuss it with you before they come to take both of us away.

По-русски: Три уровня многомерного безумия