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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…
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…
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…
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…
Propositions are supposed to be idealizations, rather like numbers or vectors or some other abstract formulation. It looks at first very powerful, and for some purposes it’s very useful. But it takes you away from enlightenment because it gives you this false sense that you haven’t understood something really until…
Having turned my back on propositions, I thought, what am I going to do about this? The area where it really comes up is when you start looking at the contents of consciousness, which is my number one topic. I like to quote Maynard Keynes on this. He was once asked, “Do you think in words or pictures?” to which he…
...basic Roman arithmetic is largely rather simple, even for those of us spoiled by Arabic notation. Addition is no sweat, because complex Roman numbers already use what math pros call additive notation, with numerals set beside one another to create a larger number. VI is just V plus I, after all. To add large…
Most real-world numbers aren’t always so nice and neat, with wholenumber multiples. If, say, Plant A grew from 2 to 3 feet, and Plant B grew from 6 to 8 feet, then we would say that Plant A grew 1/2 of its original height, whereas Plant B only grew 1/3 of its original height. Such reasoning exemplifies multiplicative…
Ms. Spooner, a long-time game player, realizes that the Racing/Grid Movement mechanic is the right choice for her students because it is particularly good at helping to assess highly granular pieces of content or skills. She envisions a game in which her students are divided into two- or threeperson teams. She wants…