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The right method of philosophy would be this. To say nothing except what can be said, i.e. the propositions of natural science, i.e. something that has nothing to do with philosophy: and then always, when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain…
Bacon s adaptation of traditional methods was to begin with observation of discrete facts, and then from observed similarities in many separate events, to arrive at generalizations—and thus he formulated his inductive method. This method ofinduction enabled him to derive rational generalizations from his observations…
The English words "man," "fish," "star," "Hower," ·run," "grow," all denote classes of objects or events which may be recognized as members of their class by very simple attributes, abstracted from the total complexity of the things themselves. Abstraction is thus almost a necessity for communication, since it enables…
A Sim in The Sims is a simple animated character, with few facial features or expressions. In The Sims 2 they seem a little more lifelike, but the improvement of the representation in some particular ways only raises the standards by which it appears to fall short in others. From the point of view of allegorithm, it…
The rules of Vice City call for a vast accumulation of cash, cars and cronies, of weapons and real estate. Most of these activities are outside the law, but law is just part of a larger algorithm. In any case, the story and the art are arbitrary, mere decoration. If in utopia, everything is subordinated to a rigorous…
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…
To grasp the proposed relationship between compression and understanding, imagine that you have a text file containing a million examples of addition, subtraction, multiplication, and division. Although any compression algorithm could reduce the size of this file, the way to achieve the greatest compression ratio…
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…
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…
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…
This “algebraic” flexibility of a word encapsulates the essence of something while leaving unnecessary concretes out. A photo doesn’t and can’t. Further, a word offers enormous flexibility in terms of input/output. It can be spoken, thought, gestured (as in sign language), written, grammatically combined with other…
The idea that space and time can be curved or warped is fairly recent. For more than 2,000 years the axioms of Euclidean geometry were considered to be selfevident. As those of you who were forced to learn geometry at school may remember, one of the consequences of these axioms is that the angles ot a triangle add up…
As an example of the power of the Anthropic Principle, consider the number of directions in space. It is a matter of common experience that we live in three-dimensional space. That is to say, we can represent the position of a point in space by three numbers. For example, latitude. longitude and height above sea…
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…
The study of mathematical uncertainty is called probability. According to Richard Epstein, "The word 'probability' stems from the Latin probabilis, meaning 'truth-resembling'; thus the word itself literally invites semantic misinterpretation." [1]What Epstein means by "semantic misinterpretation" is that if something…
Your steps should be in a cycle: short, long, long. Long in this case means a double step. Thus, you will cover five stairs in one short-long-long cycle. In addition, you should always start the first cycle on the same foot. Suppose you start on the left foot, then after two cycles you are back on the left foot…
Whenever we communicate, rules everywhere restrict our freedom to choose the next letter and the next pineapple.I Because these rules render certain patterns more likely and certain patterns almost impossible, languages like English come well short of complete uncertainty and maximal information: the sequence “th” has…
"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…
What Prensky and Gee had realized early on was that game designers had lowered the cost of failure so players would take risks. They'd figured out that well-designed problem solving that gives players a second chance and a way to share their successes is almost irresistibly attractive. In just a few years, game…
The current push to bring digital games into school is, strictly speaking, not the first, nor even the second time that educators have pushed for individualized instruction via machines. But it is decidedly the most nuanced, humanistic, and thoughtful. The first actually took place in the 1950s and early 1960s, when a…