advancedresearch.github.io
The Anti-Thoth Argument
by Sven Nilsen, 2021
In this blog post I will try to explain the anti-Thoth argument and how it relates to mathematical languages.
Daniel Fischer argued on our Discord server that ancient Egypt had a profound insight on the effects of written language.
Thoth is an ancient Egyptian deity, who was the god of the moon, wisdom, writing, hieroglyphs, science, magic, art and judgement.
Avatars
One central topic of AdvancedResearch’s study of mathematical languages is the idea of an “avatar”.
An Avatar Extension in mathematics is a method of extending a mathematical theory through symmetries.
Avatars are also important in the study of Symbols of Power, which is relevant for long-term AI safety.
Avatars in sociology and mythology of religion is a general term for influential characters and humanised beings of deities. Think about it as entities playing a role, in which whether they are real or not, is less significant than their impact on ideology.
Parallels of gender inequality
Thoth was credited all forms of knowledge in ancient Egypt, similar to Pythagoras in ancient Greece. There is a striking parallel between the two and how they are related to Seshat and Theano respectively.
Both Thoth and Pythagoras were credited inventions of knowledge without evidence. For example, in case of Pythagoras, there is no historical evidence that the Pythagorean theorem was discovered by him. You can read more about the false glorification of Pythagoras here.
One might think that this happened due to their high status in history, but this effect happened biased toward male avatars compared to female avatars.
- Seshat was an older deity than Thoth, but ended up as daughter or sometimes wife to Thoth in the mythology over time
- Theano wrote, unlike Pythagoras, but has been called the wife of Pythagoras (which she might not be)
The interesting parallel here is that when credit is unjustified, it is more likely to be attributed males than females. Furthermore, the female avatars are put in social relation to male avatars.
Gender inequality and credit of writing has an interesting history which is still relevant today. For example, Joanne Rowling put a “K” in her pen name on the books of Harry Potter, to give the initial impression that she was male.
The cursed gift to humanity
Quoting from Wikipedia’s article about the history of Toth:
Plato mentions Thoth in his dialogue, Phaedrus. He uses the myth of Thoth to demonstrate that writing leads to laziness and forgetfulness. In the story, Thoth remarks to King Thamus of Egypt that writing is a wonderful substitute for memory. Thamus remarks that it is a remedy for reminding, not remembering, with the appearance but not the reality of wisdom. Future generations will hear much without being properly taught and will appear wise but not be so.
Furthermore, Socrates argues in Plato’s dialogue that writings is silent, they cannot speak, answer questions, or come to their own defense.
With other words, writing, as great invention it might be, is viewed from the anti-Thoth position as “cursed” in some way.
This “curse” is related to the properties of writing, or lack of properties, which makes it easy to enforce biases over time.
The path semantical view
The opposite view of the anti-Thoth argument is most accurately understood through the research of mathematical languages.
Path Semantics is a research project of mathematical languages which at its foundation attempts to use an informal model of how symbols work.
The required background to understand the details would not fit inside this blog post, so I will use an metaphore from The Lord of the Rings.
Basically, Gandalf tries to prevent the Balrog from crossing the bridge, using his magic abilities:
- Gandalf is Path Semantics, constraining mathematical languages to the use of symbols
- The Balrog is the untamed, undecidable universe of mathematics
Path Semantics already has a nuanced view of the use of symbols, specially through the theory of Avatar Extensions. The untamed, undecidable universe of mathematics is barely kept in check, like hanging from a cliff by your fingernails.
However, when the anti-Thoth argument is taken to its extreme, the bridge that Gandalf and the Balrog stands on, might collapse.
Pragmatism and mathematical languages
Pragmatism is highly relevant for mathematical languages.
Take the number Pi as an example. Pi is an irrational number which symbol allows us to reason accurately about angles.
Path Semantics guarantees, although vaguely, that practical language problems related to stuff like Pi will be “solvable” to some extent. This is because even Pi is problematic from one point of view (like the Balrog), it can be “tamed” as a symbol.
Thus the Balrog is prevented from crossing the bridge. Metaphorically, we have to put Gandalf there to guard the bridge, and it is a danger because this practice is grounded in pragmatism only.
It is not a danger in the sense of everyday scenarios, but one might imagine how it could impact e.g. AI safety through obscure or esoteric semantic drifts in mathematical languages.
The anti-Thoth argument is neither pragmatic nor platonistic, but appeals to some “primitive” form of philosophical being prior to creation of the world, like the Balrog.
The problem of anti-Thoth vs Path Semantics
It is clear that written languages might be used to e.g. enforce gender inequality in a civilisation.
By extension, we do not know what impact new mathematical languages might have on society with AI technology.
If we cannot solve problems at practical level with mathematical languages, then the bridge will collapse and Gandalf must fight the Balrog.
Yet, at the same time is difficult to imagine how a civilisation might work without using symbols (e.g. Pi or Infinity).
There are two extremes, both which seems to be true or have strong arguments, but grounded in very different views of language. Neither do we know how to clearly separate these views from each other, or whether we will continue having this tension between concerns.
- How can we figure out a balance between these concerns?
- How can we think critically about this issue without making too many false assumptions?
Join the debate!
OK, so the problem is that there are strong arguments on both the anti-Thoth side and on the Path Semantics side, which I do not claim to have an answer.
The thing I am interested in, is putting this debate forward and thinking through this together.