4 ms·

Does anyone else dislike this terminology? I'm curious if there is any link at all to tensor analysis and co-variant and contra-variant vectors. (I found the te

by bryan0 6y ago

Does anyone else dislike this terminology? I'm curious if there is any link at all to tensor analysis and co-variant and contra-variant vectors. (I found the terminology confusing there too) https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors https://en.wikipedia.org/wiki/Covariance_and_contravariance_...

nelsonenzo 6y ago
The terms are mathematical terms and are applicable to both sciences. Covarient and Contravarient describe the relationship between entities in both cases here. To speak generally, if two objects have a co-variant relationship, then when one goes up the other goes up as well. If two objects have a contra-varient relationship, when one goes up, the other goes down. I'm being a bit reductive, but that's how I understand it.
- tomjakubowski 6y ago
  co-variant: the things vary together contra-variant: the things vary in opposition
gizmo686 6y ago
I may be biased since I come from a math background; but what is a clearer termonology? Covariance is when things vary in the same way; and contravariance is when they vary in opposite ways. This isn't even random math jargon; co/contra, vary, and ance are all standard english words/affixes being used for their normal meaning. In my experience, what is difficult is understanding contravariant relationships; but that is not a problem of terminology.
- bryan0 6y ago
  Yes, you might be right, this might be completely clear, and I just find it confusing for some reason but from the example in the OP I have no idea the point it is trying to get across with these terms, e.g: """ This is covariance in action: Every bike is a vehicle. (But not every vehicle is a bike.) Every bike factory is a vehicle factory. (But not every vehicle factory is a bike factory.) """ As far as for tensor stuff, I think what is confusing to me at least, is that the components of standard vectors are contravariant, while their dual covectors are covariant. contravariant tensors raise indices and covariants lower them. Anyway I'm glad this is clear to you but I find it confusing. Although I wonder now if there is a mapping from the OO diagrams in the OP with Penrose Tensor notations where everything will just make sense.... edit: missing word
qsort 6y ago
The terminology is borrowed from category theory. The partially ordered set of types can be seen as a category where the points are the types and the arrows are the is-a relation. In this setting, a covariant/contravariant type constructor is a covariant/contravariant endofunctor.
- bryan0 6y ago
  Ok thank you for this comment. I think maybe the clearer thing about categories (if I understand this right) is that the focus for covariance/contravariance is simply on the direction of the arrow. And yeah looking at the OP if you just look at the ascii diagram and the arrows it does actually seem clearer to me than the written description which seems completely confusing. but this terminology is still confusing (to me at least) and something i mentioned on another comment regarding covectors: "Contravariant functors are also occasionally called cofunctors" (https://en.wikipedia.org/wiki/Functor#Covariance_and_contravariance https://en.wikipedia.org/wiki/Functor#Covariance_and_contrav...) I guess maybe the what's confusing is that yes, it's clear these are opposites, but it's not always clear which is the original and which is dual.
  - qsort 6y ago
    Yeah, it's definitely about the "direction". I also agree with you that the OP is yet another "monads are burritos" kind of tutorial. Unfortunately it's a difficult concept to grasp and everyone has to think through it by themself in order to "get" it.

by bryan0 6y ago

nelsonenzo 6y ago

The terms are mathematical terms and are applicable to both sciences. Covarient and Contravarient describe the relationship between entities in both cases here. To speak generally, if two objects have a co-variant relationship, then when one goes up the other goes up as well. If two objects have a contra-varient relationship, when one goes up, the other goes down. I'm being a bit reductive, but that's how I understand it.

tomjakubowski 6y ago
co-variant: the things vary together contra-variant: the things vary in opposition

gizmo686 6y ago

I may be biased since I come from a math background; but what is a clearer termonology? Covariance is when things vary in the same way; and contravariance is when they vary in opposite ways. This isn't even random math jargon; co/contra, vary, and ance are all standard english words/affixes being used for their normal meaning. In my experience, what is difficult is understanding contravariant relationships; but that is not a problem of terminology.

bryan0 6y ago
Yes, you might be right, this might be completely clear, and I just find it confusing for some reason but from the example in the OP I have no idea the point it is trying to get across with these terms, e.g: """ This is covariance in action: Every bike is a vehicle. (But not every vehicle is a bike.) Every bike factory is a vehicle factory. (But not every vehicle factory is a bike factory.) """ As far as for tensor stuff, I think what is confusing to me at least, is that the components of standard vectors are contravariant, while their dual covectors are covariant. contravariant tensors raise indices and covariants lower them. Anyway I'm glad this is clear to you but I find it confusing. Although I wonder now if there is a mapping from the OO diagrams in the OP with Penrose Tensor notations where everything will just make sense.... edit: missing word

qsort 6y ago

The terminology is borrowed from category theory. The partially ordered set of types can be seen as a category where the points are the types and the arrows are the is-a relation. In this setting, a covariant/contravariant type constructor is a covariant/contravariant endofunctor.

bryan0 6y ago
Ok thank you for this comment. I think maybe the clearer thing about categories (if I understand this right) is that the focus for covariance/contravariance is simply on the direction of the arrow. And yeah looking at the OP if you just look at the ascii diagram and the arrows it does actually seem clearer to me than the written description which seems completely confusing. but this terminology is still confusing (to me at least) and something i mentioned on another comment regarding covectors: "Contravariant functors are also occasionally called cofunctors" (https://en.wikipedia.org/wiki/Functor#Covariance_and_contravariance https://en.wikipedia.org/wiki/Functor#Covariance_and_contrav...) I guess maybe the what's confusing is that yes, it's clear these are opposites, but it's not always clear which is the original and which is dual.
- qsort 6y ago
  Yeah, it's definitely about the "direction". I also agree with you that the OP is yet another "monads are burritos" kind of tutorial. Unfortunately it's a difficult concept to grasp and everyone has to think through it by themself in order to "get" it.