Exploring Typographical Systems and Formality
GEB 4
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
-T
y
-Q
z ->
C
z
.
Figure and Ground
Negative Space
!
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”)
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.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
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 )
