Monthly Archives: March 2025

Nazi Zionism

It’s easy for me to imagine a Nazi politician saying: “Get the Jews out of here. Let them have their own nation.” After all, the Jews in Palestine are blood and soil.

Digits etc

  1. There are the symbols 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. 1 is ⚫︎, 2 is ⚫︎⚫︎, etc., and 0 is nothing. When put together: For the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, xy = x * (9 + 1) + y. For example: 23 = 2 * (9 + 1) + 3. 45 = 4 * (9 + 1) + 5. And 67 = 6 * (9 + 1) + 7.
  2. Importantly, the xy in that algebraic equation isn’t another way of writing x * y. In the present context, xy means writing the symbol for the number x in front of the symbol for the number y, with the possible numbers being from ⚫︎ to ⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎, e.g. writing the symbol 2 in front of the symbol 3.
  3. Put differently: For the digits (the term “digit” meaning a certain kind of symbol) 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, the digit x written in front of the digit y = the number associated with the digit x * ⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎⚫︎ + the number associated with the digit y.

Positive and negative, plus and minus

  1. In arithmetical notation, there are the seemingly fundamental symbols +, -, *, and /. Interestingly, though: The symbols + and – are ambiguous between (1) +1 vs. -1 read as “positive one” vs. “negative one” and (2) 1 + 1 vs. 1 – 1 read as “one plus one” vs. “one minus one.” That is: + is ambiguous between “positive” and “plus,” and – is ambiguous between “negative” and “minus.”
  2. Semantically speaking, the difference between those two conceptual pairs is that a number being positive or negative is a static state, and a number being added (with a + read “plus”) or subtracted (with a – read “minus”) is a dynamic state. For example, let’s say that you’re looking at your bank account. If you have a positive bank balance (e.g., +50 thousand dollars, with the + usually being left off), then the bank owes you $50,000. And if you have a negative bank balance (e.g., -50 thousand dollars), then you owe the bank that amount of money. That’s about the static state of your bank account. But if you add or subtract money from your bank account—i.e., if you make a deposit or withdrawal—then you change the bank balance in a positive or negative direction (whether in doing so you go far enough as to change whether you’re “in the black” or “in the red”). That’s about the dynamic state of your bank account.
  3. Thus: In the logical language, there will be: (1) a symbol for the static state of being a positive number, (2) a symbol for the static state of being a negative number, (3) a symbol for the dynamic state of a number moving, or being made to move, in a positive direction, and (4) a symbol for the dynamic state of a number moving, or being made to move, in a negative direction.
  4. What about the symbols * and /, though? Interestingly, there’s no analogous ambiguity with those symbols. * is straightforwardly just multiplication, and / is straightforwardly just division.
  5. Addition and subtraction are counterpart operations in arithmetic in that what one does, the other undoes—the term “operation” here implying a dynamic state. Multiplication and division too are counterpart operations in the same sense. For example: Take 3 + 4 = 7. The start is 3, the operation is + 4, and the end is 7. Next, take that end as the start and undo what was done: 7 – 4 = 3. Analogously, consider the “doing” of 3 * 4 = 12 and the counterpart “undoing” of 12 / 4 = 3.
  6. To generalize: (1) For all numbers x, y, and z, x + y = z implies z – y = x. And (2) for all numbers x, y, and z, x * y = z implies z / y = x.
  7. It’s inelegant that the traditional notation is such that ab is the same as a * b but 22 isn’t the same as 2 * 2.