The Stripy Strudel's Journal

In a boring lecture, only three students are in the classroom. While the professor turns to the blackboard to write a long formula, five students slip away. The professor turns to the class and says disappointedly: “If two latecomers walk in, there'll be nobody left!”

This joke was funny the first time I heard it. But why is it funny, indeed? Common sense tells us that it's impossible that there are −2 students in a room. But the professor was somehow not surprised; to him −2 easily adds up with two latecomers and yields “nobody”. The problem is that we have no idea what negative two students look like and what properties they have, but it's natural for us to assume that they annihilate with positive two students.

Where does our “common sense” regarding to quantities come from? Natural numbers have properties (such as the possibility to increase any natural number by one) defined by a set of axioms, but why are these axioms exactly what they are? Natural numbers are called natural for the very reason that human invented, or, to be precise, apprehended them directly from the properties of the environment. One doesn't have to know math even at elementary school level to perceive empirically certain properties of natural numbers, for example, that 2 > 1.

For a long time, negative numbers were thought to not exist (and even zero took time to come into use), but as soon as at the dawn of Common era, such an extension to the set of numbers was first mentioned. It's not that somebody actually saw −2 students, but in bookkeeping of debts negative amounts of money or goods turned out to be quite conceivable. But if negative two swords, oxen or even slaves are possible, negative two students shouldn't seem something incomprehensible either.

The setting in the joke still seems absurd because nobody has ever witnessed a pair of positive one and negative one students being produced from nothing. But the very existence of a negative one student, or, to put it that way, lack of a student, is not absurd. One can even imagine that whole galaxies exist with negative quantities of stars, planets, universities and students. They probably call their half of the numeber axes “positive” and theorize about our existence, or, to be precise, the lack of us. (This is not the same as antimatter, despite some similarity. Antimatter exists in positive quantities, but this is rather about negative amounts of matter.)

By the way, while we're telling existential jokes, physicists shamelessly use negative quantities of electrons. A lack of electron, or −1 electron, is called an electron hole and used in analysis of semiconductors on par with an electron. Unfortunately, the number of studies of this kind in other areas of physics is negative with a large absolute value.

See also: Is logic empirical?

По-русски: Всех отсутствующих построить в одну шеренгу

It's well known that while the population of the planet grows, the total IQ stays the same. This applies to Internet users, too. As the number of users grows, the average intelligence plummets, and the software has to adapt. Let's continue the trend into the future and imagine what the browser will be like in, say, 2030. Increase this if you're optimistic, decrease if you're pessimistic.



After numerous improvements aimed at achieving user-friendliness, the browser has become as simple as it can be. It has no menus (neither main nor context), no toolbars with many buttons, no sidebars, no status bar, no dialog windows with settings. All of this was too complex for most users anyway, and scared the poor average Joe away from computers. The future browser will hardly be do a tenth of what today's browsers can do, but it will finally be usable by everyone. Speaking about visual appearance, shadows and rounded corners will still be in fashion. Thanks to the lack of any text in the interface, the browser doesn't need translation.

A browser ships with the operating system, an operating system ships with the computer. A regular user has no reason to change any of these, so the only choice among competing products that he makes is when buying a computer. This choice determines both the operating system and the browser. The browser doesn't even have a name because it's not a separately marketed product. The browser window lacks a title bar because nobody cares about the name of the program. The only button pertaining to the window itself is the red close button, and even that one looks superfluous. The window always has standard size, and web pages are usually designed for that size. Saving of pages and images as well as opening of local files is accomplished by dragging between the browser and the file manager, and printing is done by dragging to the printer.

At the top of the window is a universal field that combines an address bar, a security indicator, a window title bar and a search field. The URL is technical information uninteresting to the user; they only care on what website and what page they are. The website name is automatically verified through its certificate. The only security indication is the color of this bar: green means OK, red means problem. The user can't be expected to know about SSL or domain names, and judging whether the web page is safe enough has to be the browser's job. When it's unsafe, the main working area turns red as well because it's not easy to draw the user's attention. When the bar is clicked, it becomes white and empty, and the user can type in it. The text is always looked up in the search engine (the one with which the browser vendor has made an agreement). If an eccentric user types a URL (where would he get one in the first place?), it will work, too.

To the left of the universal field is the Back button. Its size makes it easy to find. To the right there's a button that changes its function. Usually it's Reload, but during loading it turns into a Stop button (red “No entry” sign), and while typing in the bar it's Go (green right arrow). There's no progress indicator. Instead, while the page is loading, the incomplete document isn't rendered, and the main area displays a “loading” animation instead. It's better to not render incomplete documents because their strange behavior confuses users. Fortunately, thanks to future technologies, loading will rarely take long. There are no scrollbars, either; to scroll, one grabs any part of the page that isn't a link and drags. To find text within the current page, it's enough to start typing.

The bottom part of the window contains eight slots replacing both tabs and bookmarks. Technically they're closer to tabs: each of the eight slots is like a separate browser window with its own navigation history. Clicking a slot activates it, dragging reorders, and dragging a link to an inactive slot opens the link in that slot. The active slot is marked with a contour as well as with the arrow-like shape of the main area. There are always eight slots, you can't add or remove one. A regular user doesn't need more than eight, and the controls for adding, removing and scrolling them would add unnecessary complexity. On the first start, the slots are filled with recommended popular websites, and on subsequent starts they keep their content as well as navigation history. This way, they also replace bookmarks: you can simply keep a frequently visited website in one of the slots.

For the future user, pictures are so much better than text, that's why the slots display website logos. For older websites, heuristics will be used to detect where the logo is on the page, while modern sites will be able to take advantage of the new API. The API will allow the page to tell the browser what exactly should be shown in the slot, and even update that dynamically. In the figure, Google shows the search text and the number of hits, LiveJournal shows the name of the user whose journal is open, and Gmail shows the number of unread messages; the latter keeps updating even in an inactive slot.

The split percent users who aren't satisfied with this functionality will be part of a community going further and further away from the mass market. They will have their own browsers and operating systems. Some of those who develop web services for the mass market will be parts of that community, but most webmasters will use rapid visual development tools close in spirit to the “folk's” browser.

The Russian version of this entry (see link below) features a poll. I have included English translations in the poll and encourage all readers to participate. You'll need to register a free LiveJournal account to vote.

По-русски: Минимум необходимого

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

Note: This entry is based on a joke well known in Russia; here is the English version of it that I could find.

• A spherical horse has absolutely black body.
• A spherical horse breathes ideal gas.
• The neighing of a spherical horse is a simple harmonic and spreads without dispersion.
• A spherical horse pastures in uniform fields.
• When a spherical horse prances, its trajectory is parabolic.
• The hooves of a spherical horse come into elastic collisions with a flat horizontal surface.
• A spherical horse has a non-zero probability to get out of a potential well it has fallen into.
• Mounting a spherical horse involves finding the saddle point. The resistance of the horse in this case is negligible.
• Looking from an infinitely remote stand, a spherical horse appears as a point mass.
• You can't comb the hair on a spherical horse.

UPDATE: The ideas have been used for an article in the Russian edition of Uncyclopedia.

По-русски: «На сегодняшний день у нас есть только модель победы сферического коня в вакууме»