Allegorithm is About the Relation of Sign to Number

Allegory is about the relation of sign to sign; allegorithm is about the relation of sign to number. Signs don’t open to reveal chains of other signs, pointing in all directions. Or rather, it is no longer of any importance what signs reveal. They billow and float, pool and gather, arbitrary and useless. There is no way to redeem them. But signs now point to something else. They point to number. And number in turn points to the algorithm, which transforms one number into another. Out of the...

 Computers are Associated with Precision, but Really They ...

In physics, too, where computers were used to relieve the tedium of data collection and plotting, relatively mundane applications had significant effects. When calculation was automated and its results instantaneously translated into screen visualizations, patterns in data became more apparent. Physics students described feeling “closer to science” and “closer to theory” when their laboratory classes began to use software for visualization and analysis. As in chemistry...

 Prime Numbers and Cryptography

Algorithms for finding prime numbers date back at least as far as ancient Greece, where mathematicians used a straightforward approach known as the Sieve of Erastothenes. The Sieve of Erastothenes works as follows: To find all the primes less than n, begin by writing down all the numbers from 1 to n in sequence. Then cross out all the numbers that are multiples of 2, besides itself (4, 6, 8, 10, 12, and so on). Take the next smallest number that hasn’t been crossed out (in this case, 3), an...

 Recursive Self-Improvement in Human Civilization

Let’s consider Arabic numerals as compared with Roman numerals. With a positional notation system, such as the one created by Arabic numerals, it’s easier to perform multiplication and division; if you’re competing in a multiplication contest, Arabic numerals provide you with an advantage. But I wouldn’t say that someone using Arabic numerals is smarter than someone using Roman numerals. By analogy, if you’re trying to tighten a bolt and use a wrench, you’ll do better than someone...

 Where's Transparency With So Many Layers of Abstraction?

Some older scientists, for example, justify their use of opaque software by pointing to the infinite regress of computer representations. After all, they argue, it doesn’t really mean much to know how your simulation is programmed if all you are looking at is a high- level computer language. The “real guts” of the program is in assembly language and in all that lies beneath that, and no one wants to go to that level with today’s complex machines. In the 1980s, Professor Barry Nilo= in...

 Why numbering should start at zero

When dealing with a sequence of length N, the elements of which we wish to distinguish by subscript, the next vexing question is what subscript value to assign to its starting element. Adhering to convention a) yields, when starting with subscript 1, the subscript range 1 ≤ i < N 1; starting with 0, however, gives the nicer range 0 ≤ i < N. So let us let our ordinals start at zero: an element's ordinal (subscript) equals the number of elements preceding it in the sequence. And the ...

 The Pleasure of Entrainment

If entrainment is a form of pleasure, it is a pleasure at once structural and experiential, both mathematically regular and playfully flexible. Entrainment is not a phenomenon completely unique to games, but it does come very close to identifying the curious structural pleasure that all game experiences seem to contain: the meditative patterns of Tetris; the turn-taking, clacking cadence of Billiards; the rhythmic shooting pattern of Space Invaders; the pulsing flow of cards, hits, and chips ...

 A Computer Algorithm for Randomization

Back in the early days of computers, one of the more popular methods of generating a sequence of random numbers was to employ the following scheme: 1. Choose a starting number between 0 and 1. 2. Multiply the starting number by 4 ("stretch" it). Subtract 4 times the square of the starting number from the quantity obtained in step 2 ("fold" the interval back on itself in order to keep the final result in the same range). 3.Given a starting number between 0 and 1, we can use the proce-dure�...

 Complexity in Systems

On the far left are fixed systems that remain unchanging.hand, a screen that is full of random static would be completely The relationships between their elements are always the chaotic, with the color of a dot at one moment having nothing same. The black, unchanging TV screen is a good image for this kind of system. To the right of fixed systems in the chart are periodic ones. Periodic systems are simple systems that repeat the same patterns endlessly. The simple two-building version of the...

 Euclid's Elements as a Game

"If video games had been around in 350 BC, Euclid would have made a video game," Devlin told me. The thirteen books of Euclid's Elements would have been the supplemental material, a PDF file that you could read if you wanted to. "People think I'm joking—I absolutely mean that. Euclid would not have written a textbook, he would have designed a video game." Peek at any of his proofs, Devlin said, and you'll quickly find that the great Greek mathematician, often called the father of geometry, ...