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...

 Roman Arithmetic

...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 numbers, simply pile all the letters together, arrange them in descending order, and there’s your sum. CLXVI plus CLXVI? CCLLXXVVII, or CCCXXXII. And one of the advantages of the Rom...

 Math Games

Buzz. An example of a low-stress, win-win game is Prime Number Buzz. Students stand in a circle or at their desks and go around the room in order, saying either the next sequential number if it is a composite or “buzz” if it is a prime. If they are incorrect, they sit down, but they keep listening and when they catch another student’s error, they stand up and rejoin the game. (The same game format works for Multiples Buzz, using multiples of, for example, 3, 4, and so on.) Telephone. T...

 Delay Method of Errorless Math Practice

Prepare a list of the calculations from the flash cards on a sheet of paper. These can be on a template, with multiplication facts at the appropriate level pulled and copied for the student. On these forms, include three columns next to each multiplication question, labeled “correct repeat,” “correct wait,” and “correct response.” Start with review and confi dence building. For example, show the question 3 × 4 = __ on the card and without any delay say the answer. Th e student re...

 The Origin of Chaos Theory

Lorenz and his team were working to develop a weather forecasting program on an early computer known as a Royal McBee LGP-30.21 They thought they were getting somewhere until the computer started spitting out erratic results. They began with what they thought was exactly the same data and ran what they thought was exactly the same code—but the program would forecast clear skies over Kansas in one run, and a thunderstorm in the next. After spending weeks double-checking their hardware and t...

 Argument for Decimal Currency

[Decimal currency is desirable because] by that means all calculations of interest, exchange, insurance, and the like are rendered much more simple and accurate, and, of course, more within the power of the great mass of people. Whenever such things require much labor, time, and reflection, the greater number who do not know, are made the dupes of the lesser number who do.