LLMs are Lossy Compression for the Entire WWW

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 would probably be to derive the principles of arithmetic and then write the code for a calculator program. Using a calculator, you could perfectly reconstruct not just the million ex...

 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...

 History of the Concept of Art

Nowadays when someone speaks of "art" you probably think first of "fine arts" such as painting and sculpture, but before the twentieth century the word was generally used in quite a different sense. Since this older meaning of "art" still survives in many idioms, especially when we are contrasting art with science, I would like to spend the next few minutes talking about art in its classical sense. In medieval times, the first universities were established to teach the seven so-called "liber...

 Number Scrabble: Numerical Tic-Tac-Toe

In psychological research on problem-solving, sometimes the game of Tic-Tac-Toe is employed, which, though very simple to learn and play, still offers sufficient problems to the investigator in that it is not at all clear what heuristics are used by the subjects, except avoiding the winning move of the opponent. The same is apparently true for the isomorphic game of Number Scrabble, which is based on the fact that there exists a 3 X 3 magic square, of which rows, columns, and main diagonals a...

 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...