I think it’s kinda a weird translation. To be something is to have a relationship with the thing that one is, like an identity relationship, one is one, 1=1 for example. A one way equals sign would communicate to me something like (square)=>(rectangle) to represent that all squares are rectangles, while emphasizing that they do not represent the same thing, as they do not use a standard equals sign, as that would imply a shared identity.
That’s just me spitballing though, I definitely can’t read that character or understand the language. I’m just assuming that your translation is accurate and following the context clues to their logical conclusion.
In most languages, "to be" is used to express at least 3 kinds of relationships, which can be distinguished depending on whether the words connected by "to be" are e.g. pronouns, proper nouns or common nouns:
1. identity: "He is John"
2. membership: "He is engineer"
3. inclusion: "Wolves are carnivores"
For the non-symmetric membership and inclusion relationships, in natural languages the order of the words does not really matter, because a speaker will recognize which of the 2 words connected by "to be" corresponds to a bigger set, of which the other word may be a member or a subset, so "he is engineer" and "engineer is he" will be understood to mean the same, even when one alternative sounds weird (i.e. Yoda speech).
This is why, unlike for the agent and patient of a transitive verb, which need special markers, e.g. the nominative and accusative case markers, in the languages that do not have a fixed word order, for the subject and the nominal predicate that are connected by "to be" no distinct markers are required, they can use the same case (e.g. nominative), because they can always be recognized regardless of their order.
"To be" can also express other relationships, like position in space or time, qualities or quantities and so on, all of which are also distinguished by the kinds of words that are connected by "to be".
In an unambiguous language, like in formal mathematics or in programming, each kind of relationship should use a different notation.
That makes sense. It would really have to be read in context to tell how poorly it might read. I didn’t mean to say it was bad, just saying that I understand the confusion.
Were you around for the thread about if LLMs “know” things? It would have benefited from more precise language.
In English, it's words like "is", "was", "are" or the verb "be". It follows the rules of linguistics, not mathematics, so there shouldn't be pressing need to stress its non-commutativity.
That's helpful context, but I didn't really consider them separate contexts for the purposes of using context clues to try to understand it. I thought you didn't know what that part might mean. What did you mean?
In most Japanese lessons in English, when you are introduced to だ/です/である, it is simply explained as being like "is", or if they've already set a rule that sentences end in verbs, it's introduced as the verb "to be". That conveys, rightly or wrongly, all the things English speakers understand about "is".
This Japanese lesson starts with the assumption that part of the "だ" hiragana looks like "=", which I already don't agree with! Even the dakuten (゛) on the character looks more like an equals than the swooshy bowl they're comparing to "=".
It then says that だ is comparable to equality and mathematical equations, rather than like the lingual is/are/be, and then has to qualify that the equality is non-commutative. They could've saved time by not making that comparison, and instead comparing with is/are/be, which English speakers already understand is not commutative. "John will be early" != "Early will be John" (unless Yoda, you are)
I haven't studied many languages, but there's something about the flavor of so-called "foreign" language learning which is culturally anchored to the language of the teaching materials themselves. I wonder if these issues you have about comparisons that don't make sense and so on are about your own personal context and point of view, or if the issues reveal some differences between native Japanese teaching methods versus Japanese as she is taught to typical English language learners.
That’s just me spitballing though, I definitely can’t read that character or understand the language. I’m just assuming that your translation is accurate and following the context clues to their logical conclusion.