I was thrilled the other day to see in this blog post
Leibniz’s symbol for “=”: Π
From the post:
“There’s Π as an equals sign instead of =, with the slightly hacky idea of having it be like a balance, with a longer leg on one side or the other indicating less than (“<”) or greater than (“>”)”
In fact, Leibniz’s notation Π, with 2 lines of equal height and a top crossbar, is a very good representation of our actual experience with equal things—people of equal height, for example. Because it represents the structure of reality better, it is a clearer, better symbol than “=”. I surmise that Leibniz appreciated this, though the blog author Wolfram doesn’t, and even disses Leibniz’s reasonable improvements for “<” and “>”.
A relevant quote from Korzybski’s Science and Sanity, p. 59:
“As words are not the objects they represent, structure, and structure alone, becomes the only link which connects our verbal processes with the empirical data . . . (therefore) we must study the structural characteristics of this world first, and, then only, build languages of similar structure, instead of habitually ascribing to the world the primitive structure of our language.”
According to Kodish in his Korzybski biography, “Korzybski defined structure as a complex of relations consisting of multidimensional order.”
(Korzybski, by the way, considered his work an extension of Leibniz’s, and that with it “The dreams of Leibniz will become a sober reality.”)
My ideograms, as visual, graphic concepts, aim, where possible, to reflect the structure of the realities they represent. This idea of a graphic representation or other idea being structurally similar to reality deserves, I think, a term. I’ll call it “rectistructural”. Π is more rectistructural than = and is therefore superior—more accurate, more useful, more conducive to clear, effective thought. Wolfram hints at this: “To me it’s remarkable how rarely in the history of mathematics that notation has been viewed as a central issue. . . . And I suspect that Leibniz’s successes in mathematics were in no small part due to the effort he put into notation, and the clarity of reasoning about mathematical structures and processes that it brought.”
With neoideograms I am building a language that is structurally more similar to reality than conventional language. Often I am stumped and have to posit an arbitrary convention, but that’s unavoidable.
Wolfram says that Leibniz “talked about decomposing ideas into simple components on which a “logic of invention” could operate.” Neoideograms are a step in this direction.
Wolfram also says that “despite all his notation for “calculational” operations, Leibniz apparently did not invent similar notation for logical operations.” As far as I know present day symbols for logical operations have no relationship to the structure s of the realities concerned—they are not rectistructural. I’m optimistic that I can come up with reasonable first attempts at rectistructural ones—so that the “or” sign actually resembles what happens with the “or” operation, for instance. We’ll see.