A repo to track the historical evolution of notational systems in arts and sciences.
Petroglpyhs by ancient humans are probably the first ways of creating a map of communication with fellow beings.
8th century script that became the calligraphic standard.
John Wilkins
https://klaustruemper.com/2018/02/17/circular-slide-rule-based-on-burgis-logarithm-tables-of-1620/
Llull’s work would influence a key figure in the history of science: Gottfried Leibniz. In his dissertation on combinatorics, De Arte Combinatoria, influenced by Descartes’ idea and Llull’s rotating wheels, he proposes an alphabet of human thought.
Leibniz did work with binary arithmetic.
He turned to I Ching for his inspiration. He used 0 to denote the broken line representing chaos and 1 to denote the straight line representing order in the ancient text.
In print, the notation first appeared before public in Nova methodus pro maximis et minimis, itemque tangentibus, qua nee fractas, nee irrationales quantitates moratur, & singulare pro illis calculi genus in Acta Eruditorum (Pages 467-473) in 1684.
There is also an upside down ± symbol present in the text which is curious.
Leibniz purportedly made use of the integral sign in his private notebooks (LH 35, 8, 8).
This notation first appears in print for public in De Geometria Recondita et analysi indivisibilium atque infinitorium in Acta Eruditorum (Pages 292-300) in 1686.
Instead of the italic long s, the serif version can be found to represent the symbol in print.
Made triangle diagrams based on Lambert’s line diagrams
Used circle diagrams to illustrate rules of conversion
Arthur Cayley was the first person to coin the ideas of finite group and trees. It is also very interesting that he played around with visual notations to convey ideas about these algebraic structures.
- Original Paper
A programming language to play around with Begriffsschrift notation:
He seems to have a logical matrix in his book and also, need to create a catalog of the notations he has employed in his other works such as many valued logics.
Stam seems to be the first person to publish work on Sheffer Stroke and Pierce Arrow: https://twitter.com/rrrichardzach/status/1251532455829319680
Research who brought in the sequent calculus deduction method to the forefront of computer science deduction methods.
This one needs deeper investigation as it is much close to box-X notation of Charles Peirce, XLA notation of Shea Zellweger, and Randolph diagrams. Much interesting about this idea is that he had a certain philosophical grounding and use of brackets to complement this notation for operators.
Inverted representation of T for falsehood.
Randolph Diagrams were used to notate Boolean operations in a 2 by 2 grid. This can be extended to more than one truth values.
These might have precursors in X-frame notation of Peirce in “A Proposed Logical Notation (1903)”. Detail from this paper
Karnaugh maps are used to notate Boolean algebra. This is an improvement upon Veitch Chart which is a rediscovery of Marquand Diagrams introduced by Allan Marquand.
A book surveying logical machines and diagrams
2020
Adele Lopez (2020)
Ivan Reese (2019)
A web based proof assistant for globular n-categories. Considered to be the successor to Globular
A visual editor for opetopes.
Drever’s playground for George Spencer-Brown’s notation from Laws of Form.
His take in simplifying Maxwell’s equations could also be helpful in understanding the intellectual framework shift that helped in changing the perspective on functions.
A good paper tracing the history of trees in Mathematics
Visual information and valid reasoning
Diagrammatic Reasoning: Cognitive and Computational Perspectives
A History of Logic Diagrams (2012)
Legg (2013)
A.W.F. Edwards (2006)
Peter Bernhard (2001)
P. Bernhard (2007)
Umberto Eco
A fun tool to generate a rune like language: https://watabou.itch.io/rune-generator
Books that take a largely diagramattic approach in its pedagogy. For more information check out
Rocco Gangle
Frederik Stjernfelt
Mateja Jamnik
Mark Greaves (2002) Has a compilation of Euler style and other logic diagram sunder the heading ‘Early diagrams for Syllogistic Logic’
A tour de force of the different kinds of notational devices and spatial thinking tools that humans have employed over the course of history to make sense of the world around them. Note to self: I need to take the spectrum of ideas presented there and incorporate them as categories in this document.
List of links of techniques to help enhance mathematical notation