Exploring Typographical Systems and Formality
Delve into the intricacies of typographical systems and formal rules, where symbols and theorems are defined through unique structures and operations. From designing a system based on prime numbers of hyphens to capturing the concept of divisibility, this journey uncovers the complexity and creative possibilities within typographical frameworks.
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Presentation Transcript
Key idea from the pq-system Typographical operations can code complex things
Typographical Reading and recognizing any of a finite set of symbols Writing down any symbol belonging to that set Copying any of those symbols from one place to another Erasing any of those symbols Compare whether two symbols are the same Memorizing a list of previously generated theorems
Goal today Design a typographical system where: P--, P---, P-----, P------- (P followed by a prime number of hyphens) are theorems (a wrong number results in non-theorems)
At least, multiply --t---q------
C? Rule: x-Ty-Qz -> Cz.
! There exists formal systems whose negative space is not the positive space of any formal system.
Capturing P Define a notion of does not divide (equiv. is not a multiple of ) in the system Now we need to check this for every possible divisor. Need a checkpoint ( is divisor-free up to )
