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Mathematics in toki pona

seme

· 1 coffee

toki pona

FAQ

Frequently asked questions about toki pi (nasin nanpa).

Why not use ijo symbol instead of ijo symbol?

These are NOT the only symbols you can use for this. Far from it, in fact.
  • It would make more intuitive sense to use wan for addition, but then using tu for subtraction could sound strange.
  • You could use sin instead for multiplication or addition.
  • You could use ala for subtraction.

The symbols you chose are weird.

I really think this is not as important as people make it out to be. If you think there is a difference between multiplication and addition, let me remind you that \[(\mathbb{R}_{> 0}, \times) \cong (\mathbb{R}, +).\]

Why did you choose those symbols in specific?

A distinction that I would like to make clear is that, in the language of Mathematics, there is a general difference between the "product" and "sum" of something. I think this is best expressed in examples:
  • algebra of sets:
    • \(A \cap B\) := product
    • \(A \cup B\) := sum
  • boolean logic:
    • \(a \land b\) := product
    • \(a \lor b\) := sum
  • order theory:
    • \(\inf\{a, b\}\) := product
    • \(\sup\{a, b\}\) := sum
  • algebraic data types (Haskell):
    • (a, b) := product
    • a | b := sum

Boolean logic, being the closest to natural language in my opinion, has the clearest example of what a general “product” and “sum” expresses. The “product” should express the notion of “both” things and “sum” should express the notion of “either” things.

With this in mind,

  • I am using namako for addition because it expresses “additonal” or “extra” things.
  • I am using weka for subtraction because of the dual reasons of namako.
  • I am using wan for multiplication because it expresses the idea of “both” things that a “product” should express.
  • I am using tu for division because of the dual reasons of wan.

Isn't it confusing that wan and tu refer to a number and an operation?

Yes.
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