The only thing I have not understood in this word-to-word is the translation of Ernst as "honest". Wouldn't it mean "seriousness" here ?
"That is surely not your seriousness" does not sound far from "You cannot be serious" and it makes the sentence easier to understand, at least to me.
I have compared "Das ist nicht dein Ernst." with "Das ist nicht ja wohl dein Ernst." and "ja wohl" seems to help express a sense of surprise or incredulity, similar to what might be conveyed by the English "You, of course, cannot be serious!!" Any native speakers want to confirm or contradict this idea?
"ja" and "wohl" do not mean "yes" and "well" in this context. They are modal particles, which reflect the mood or attitude of the speaker and/or highlights the sentence focus. Often they are not translated to English. Reference: https://en.wikipedia.org/wiki/German_modal_particles
The closest literal translation to English is "That is not your seriousness" .
I asked the same at https://german.stackexchange.com/questions/55063/das-ist-ja-wohl-nicht-dein-ernst-meaning-of-particle-ja/55066. Although not even the Germans in Stack Exchange reached a consensus about the exact meaning, my understanding is that emphasizes that the following statement is known/obvious. Although German modal particles are often not translated to English, a similar feeling of "ja wohl" would be expressed in English with the word "obviously".
Yes, but it should be "You cannot be in earnest." See the following for when you use "cannot" and when you use "can not": http://www.oxforddictionaries.com/us/words/cannot-or-can-not
"You can't be in earnest" is also fine.
Is "ja wohl" strictly necessary in this sentence? Would "Das is nicht dein Ernst" do as well?
It's not grammatically necessary, no.
Das ist nicht dein Ernst. = You are not serious.
It's the difference between "You are not serious" and "You cannot be serious / You are surely not serious" or between "You are kidding" and "You must be kidding / You have got to be kidding".
It's part of the expression. Unfortunately idioms usually just have to be learned.
Sort of like "he bought the farm" being an expression in US English for someone having died. As well as a being a sentence meaning someone actually buying/purchasing a farm. I never quite understood how that particular idiom came about. Some, one can sort of figure out. But others are just weird.
this one defeated me so effing hard that I think this is where I take a break and come back tomorrow. I can't even begin to decipher this since Duo gives no explanation of "ja wohl" anywhere. Apparently "wohl" means "well-being" according to DL and ja is "yes." how does this lead to "you cannot be serious."
You can always try a dictionary like dict.cc or pons. Using just one source to learn a language generally does not work.
Also, while "Wohl' with a capital "W" is a noun and means "wellbeing/welfare/good (as in 'the good')", "wohl" with a lower case does not.
With a lower case "w" "wohl" is an adverb meaning things like "indeed/surely/arguably/...' and more like it.
In German you really need to pay attention to capitalization since it can change the meaning.
And as far as idioms like this go, unfortunately, they just need to be learned/memorized, in any language. English has a huge amount of weird ones that don't really make any sense such as "he bought the farm" meaning "he died" if used as an expression and not a statement of purchase. If translated literally into any other language it would just mean that someone/he purchased a farm.
Thanks for the link and the advice! My biggest frustration about the idioms given on DL is that they are thrown in without any context. I wish they could provide the literal translation as well so that we can see how the key words are being used in the sentence and then try to connect the literal translation to the actual meaning of the idiom. Thanks again for your help :)
It can get a bit frustrating when getting things wrong, especially if it was not reviewed in the "Tips & Notes". What I tell myself though is that overall Duo is very good, especially at keeping you coming back unlike many other programs. Not to mention free. (It is a bit hard to complain too much about something that is provided for free and actually works.)
Also, often one can learn/remember something really well by getting it wrong. It tends to stick in one's memory. At least it does in mine. And since Duo does not hand out grades it does not matter how often one misses something. (At least on the web version which I use. From what I read in comments the app has "hearts" and if you lose a certain number one has to take a break. The web version does not do that. It just keeps going and works just fine in a browser on a mobile device.)
If you want something more structured you could try "Deutsche Welle". It is a German news site (also has an English version) and has a whole section devoted to teaching/learning German. It is very, very good. It also has more grammar than Duo and most other online sites, as well as something called "slowly spoken news/Langsame Nachrichten" which are news stories spoken more slowly by people (professionals) with excellent diction. It's not quite as game-like as Duo though, more like regular lessons/school, so it may require a bit more discipline.
https://www.dw.com/en/top-stories/s-9097 (main site)