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...

 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 Exercise: Multiple Approaches to Problem-Solving

For example, if the problem was to fi nd the answer to 8 × 6, students may suggest three options: memorizing the multiplication table for 6, knowing that 8 × 5 = 40 and adding another 8 to equal 48, or adding a column of six 8s. Allowing students to personally choose among approaches all confi rmed as correct and to support their choice will increase their comfort levels. Th is process also builds math logic, intuition, and reasoning skills that extend into other academic subjects and real-...

 Mathematical Cue Words

Addition: add, plus, sum, total, altogether, increased by, grew, gained, total of, combined, more than (as in, “3 more than 7 is 10”), put together, in all Subtraction: minus, take away, diff erence, less than, from, remove, subtract, gives away, sells, loses, fewer than, decreased by, diff erence between Multiplication: product, times, doubled (tripled, etc.), some problems give information about one and ask for total amounts (also, when dealing with multiplication of fractions, of us...

 12 Tone Equal Temperament

On a standard piano keyboard, one octave is divided into 7 whole tones: A, B, C, D, E, F and G. In between these tones are 5 further notes which can be called either sharps or flats: A# (Bb), C# (Db), D# (Eb), F# (Gb), G# (Ab). (whether it's a sharp of a flat doesn't really matter, the note has the same frequency, just a different name). This gives us a grand total of 12 notes in one octave. If you were to measure the frequency of a note, then measure the frequency of a note exactly one octa...

 RPG as Cooperative Experience

A role-playing game is a cooperative experience between multiple participants. At its simplest, it can be described as an organized form of group make-believe, with a set of rules and procedures to keep things consistent and fair. The goal is not to win - there are no real "winners" in a role-playing game - but simply to have a good time.