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These improper nouns are unfortunately common in mathematics. Terms like “real number” are often confusing to non-mathematicians, who assume a deeper meaning be

by xigoi 4y ago

These improper nouns are unfortunately common in mathematics. Terms like “real number” are often confusing to non-mathematicians, who assume a deeper meaning behind them. This is why we need Lojban.

twawaaay 4y ago
As a bit of a mathematician (well... "studied theoretical math" would be more accurate), mathematics would not function without those names. And no, Lojban would not help. In math you build abstractions on top of abstractions on top of abstractions on top of abstractions to the point where you a single word can carry so much meaning you may need years of study and a whole shelf of books dedicated to the subject just to understand it in its entirety. Unwinding whole meaning of the term would be absolutely impractical. No, we don't need Lojban. Shorthands are making it easier to work with math, not harder. If you are newbie and you want to understand any of it I can assure you, the complete description of the term without using any abstraction would be completely meaningless to you anyway. Slowly learning those abstractions and building up to what you want to understand is still the best, easiest way.
- xigoi 4y ago
  Thanks, but I'm not a newbie by any means. Yes, names are necessary. I just wish there was a clear indication that they are names. Nobody is confused by the term “Dedekind cut” because it's clearly a name. This is partly a fault of English (or other natural languages) and partly of math nomenclature.
vharuck 4y ago
Interesting factoid: "real numbers" are called that to distinguish them from "imaginary numbers." The latter term was not meant as an improper noun, but a proper insult. Some mathematicians called them imaginary to imply that branch of mathematics had no basis or use in reality. The term stuck, even though we found plenty of uses.
- xigoi 4y ago
  Well, that's not the first time something like this happened. An ancient mathematician was murdered for discovering irrational numbers, and the name given to them is also quite insulting.
bmacho 4y ago
There is an assumption in mathematics that if we use an adjective with a noun, it will specialize the noun, that is, it adds an additional constraint to it, yet it remains to be the original noun as well. (In other words, the Liskov substitution principle holds.) It is almost always wrong. An adjective can generalize the noun, which is funny, because in that case either the adjective or the noun must be wrong. It's called the "red herring principle"[0], that is, red herrings are not red, or are not herrings. Like:[1] - a manifold with boundary is not a manifold, or it doesn't have a boundary, but can't be both - a nonassociative algebra, is either associative, or not an algebra - multivalued functions, partial functions, contravariant functors, noncommutative geometries, etc etc etc [0] : https://ncatlab.org/nlab/show/red+herring+principle https://ncatlab.org/nlab/show/red+herring+principle [1] : https://ncatlab.org/nlab/show/red+herring+principle#examples https://ncatlab.org/nlab/show/red+herring+principle#examples
Bakary 4y ago
If a non-mathematician is confused in this way, they won't be able to use the concept for anything useful anyway. I'm saying this as a non-mathematician.

by xigoi 4y ago

twawaaay 4y ago

As a bit of a mathematician (well... "studied theoretical math" would be more accurate), mathematics would not function without those names. And no, Lojban would not help. In math you build abstractions on top of abstractions on top of abstractions on top of abstractions to the point where you a single word can carry so much meaning you may need years of study and a whole shelf of books dedicated to the subject just to understand it in its entirety. Unwinding whole meaning of the term would be absolutely impractical. No, we don't need Lojban. Shorthands are making it easier to work with math, not harder. If you are newbie and you want to understand any of it I can assure you, the complete description of the term without using any abstraction would be completely meaningless to you anyway. Slowly learning those abstractions and building up to what you want to understand is still the best, easiest way.

xigoi 4y ago
Thanks, but I'm not a newbie by any means. Yes, names are necessary. I just wish there was a clear indication that they are names. Nobody is confused by the term “Dedekind cut” because it's clearly a name. This is partly a fault of English (or other natural languages) and partly of math nomenclature.

vharuck 4y ago

Interesting factoid: "real numbers" are called that to distinguish them from "imaginary numbers." The latter term was not meant as an improper noun, but a proper insult. Some mathematicians called them imaginary to imply that branch of mathematics had no basis or use in reality. The term stuck, even though we found plenty of uses.

xigoi 4y ago
Well, that's not the first time something like this happened. An ancient mathematician was murdered for discovering irrational numbers, and the name given to them is also quite insulting.

bmacho 4y ago

There is an assumption in mathematics that if we use an adjective with a noun, it will specialize the noun, that is, it adds an additional constraint to it, yet it remains to be the original noun as well. (In other words, the Liskov substitution principle holds.) It is almost always wrong. An adjective can generalize the noun, which is funny, because in that case either the adjective or the noun must be wrong. It's called the "red herring principle"[0], that is, red herrings are not red, or are not herrings. Like:[1] - a manifold with boundary is not a manifold, or it doesn't have a boundary, but can't be both - a nonassociative algebra, is either associative, or not an algebra - multivalued functions, partial functions, contravariant functors, noncommutative geometries, etc etc etc [0] : https://ncatlab.org/nlab/show/red+herring+principle https://ncatlab.org/nlab/show/red+herring+principle [1] : https://ncatlab.org/nlab/show/red+herring+principle#examples https://ncatlab.org/nlab/show/red+herring+principle#examples

Bakary 4y ago

If a non-mathematician is confused in this way, they won't be able to use the concept for anything useful anyway. I'm saying this as a non-mathematician.