"at" vs. "til at"
Yep, another question about this. It's been discussed a lot in the past, but explanations I've seen have seemed to me not very systematic (and duo's terrible search feature makes it frustrating to try to find them all).
So, consider this sentence from duolingo: "Det er umuligt at forstå dine definioner af enheden." (It is impossible to understand your definitions of the unit).
Why can one not say "Det er umuligt til at forstå...? I'm hoping for a general explanation that applies to most/all relevant sentences, not just this example.
This issue is a major difficulty for English speakers trying to learn Danish. If someone can provide a satisfactory general answer, mods might consider putting it in a "stickied" thread, for easy reference.
Any answers much appreciated!
In Danish, the infinitive always includes "at", like "at forstå", "at spise" and "at føle".
There are also extended infinitives, like:
Ved at: which describes 1. how something is done ("Han vækkede hende ved at hælde vand i sengen"; He woke her up by pouring water in the bed), or 2. something that is/was just about to happen ("Jeg var ved at spise aftensmad"; I was just about to eat dinner).
For at: which describes a motive; it's comparable to "in order to" ("Vi har brug for træer for at leve"; We need trees [in order] to live / "Vi lærer dansk for at få et job"; We learn Danish [in order] to get a job).
And of course, til at.
It's usually either part of a fixed expression (jeg glæder mig til at..., jeg behøver tid til at..., jeg er klar til..., etc.)
In some other sentences, usually those describing ability (f.eks jeg er god til at cykle), til is not part of the "til at" extended infinitive, but rather it is attached to the adjective "god".
But "til at" is also used when something requires you to take action/do something else.
So "til at" is not used in "Det er umuligt at forstå dine definioner af enheden", because no action is required to be taken in the sentence; it is just a statement (of the impossibility to understand the definitions). However, "til at" would be used in the following sentence: "Hjælp os til at forstå hvornår 'til at' bruges" because the plea for help is compelling someone to take action.
Another example of the usage of "til at": "Harry fik lov til at spise resterne, mens onkel Vernon købte Dudley en større portion" (Harry was allowed to eat the leftovers, while Uncle Vernon bought Dudley a bigger portion). "Til at" is used here because Harry is being allowed/enabled to eat the leftovers.
Or "Denne dreng var en anden god grund til at holde dem på afstand" (This boy was another good reason to keep them at a distance). "This boy" is requiring the action of "keeping them [the Potter family] at a distance".
And finally, another example from Duolingo: "Mange vampyrer opdrages til at drikke blod fra dyr" (Many vampires are raised to drink blood from animals). Vampires drinking blood is necessitated by the way they have been raised.
A huge thank you goes to FloatingBrick for being super patient and explaining this to me!
Let's start with til at
When preceded by an adverb, it can either translate to: "at"+ present participle.
"Jeg er god til at cykle" = "I am good at biking" (Lit: "I am good at to bike") or: "to" + stem. (i.e infinitive) "Jeg er klog til at falde for det trick" = "I am too smart to fall for that trick"
When preceded by a subject+verb, then we are talking about a tool for getting a result and it translates to: "for" + present participle. "Et piskeris bruges til at piske med" = "A whisk is used for whipping/whisking"
In combination with "fra at", it is used tell what status is after a change: "Han gik fra at være rig til at være fattig" = "He went from being rich to being poor"
When we talk about actions for getting a result, we use "for at" instead of "til at". "Jeg kører for at komme til et andet sted" "Jeg spiser for at overleve"
1. "Jeg var ved at falde" = "I was about to fall" = almost did the action, but managed to avoid it.
- "Jeg var ved at træne" = "I was traning" = did the action of.
Here you can also use the simple past "Jeg trænede" or the longer "Jeg var i gang med at træne" (lit: "i was in the ongoing action of training"
You can tell the difference by looking at the subsequent verb. If it is something that you do by accident, but never by intend. it is case 1. If it it something cannot do by accident, but always by intend, it is case 2.
When used transitively, it can sometimes be ambiquous:
"Jeg var ved at spise bananen".
You cannot eat by accident, but you can accidentally include the banana.
It can be translated to "I almost ate the banana by accident" (case 1)
or "I was eating the banana" (case 2)
- "Jeg fik svaret ved at spørge" means "I got the answer by asking" = by the mean of/due to. In this case there are no alternative.
This combination has only a few uses. If you are doing something and wants someone to join in order to make it go faster or be easier, we use "hjælpe (pronoun) med at" "Vil du hjælpe mig med at skrælle kartofler" = "will you help me peel potatoes"
You can form the sentence by using "ved at" instead, but it will change the meaning a bit.
"Vil du hjælpe mig ved at skrælle kartofler" = "Will you help me by peeling potatoes".
In this case no one is doing it, and you are asked to do it"
There are cases where "til at" is used instead, but with a different meaning.
"Vil du hjælpe mig til at forstå bogen" = "Will you help me, by making me understand the book"
In this case your help is needed in order to get anywhere.
In some cases it is either irrelevant who you are helping, or it might benefit a whole team.
In this case you skip the pronoun.
"Vil du hjælpe med at skrælle kartofler" (join in)
"Vil du hjælpe ved at skrælle kartofler" (do it yourself, at least for a start)
The second use is "begynde/starte med at" It is used to tell what the first step will/should/could/must be. "Du kan starte med at dække bordet" = "You can start by setting the table"
The last use "ende/slutte med at" the same with "begynde/starte med" expect we are now talking about the last step.
You can also encounter fixed combinations:
være med til at
"Vil du være med til at spille fodbold" = "Will you participate in playing soccer"
Here it is not about helping, but a simple question/request about you participating.
or it kan be used to tell ask/tell what/whether you are participating in:
"Jeg er med til at bygge huset" = "I am participating in building the house"
"Er du med til at bygge huset" = "Are you participating in building the house"
hjælpe til ved/med at
This is used when someone wants to help, to suggest how they can be a help:
"Du kan hjælpe til med/ved at plukke jordbær" " You kan help (by) picking strawberries"
blive ved med at
This is about continuity
"Det vil blive ved med at regne hele natten" = "It will keep raining al night"
And then there are cased where the words are seperated by a comma. "begynde/starte med, at" "ende/slutte med, at" "være med til, at" "med, at"
The comma is required when there is a subject after "at" e.g. "Vi kan starte med, at John fejer gulvet" = "We can start with John sweeping the floor"
And finally there is a few cases with "ved" where the comma is mandatory. In these cases "ved" means "know" or is related to it. Although it is not an preposition/adverb here, you might encounter them with out the comma, due to a common mistake when setting punctuation marks.
"Jeg ved, at du er rig" = "I know that your are rich"
"Jeg vil ikke være ved, at jeg er glad for at gå i lyserøde bukser" = "I will not let it be known that I like to wear pink pants"
"Jeg vil ikke stå ved, at jeg tisser i sengen" = "I will not admit (to myself) that I am a bedwetter". Here you know it is true , but you are trying to convience yourself that it is not true.
Though not containing "ved", it is very related to the two previous uses: "Jeg vil ikke indrømme, at jeg fryser" = " I will not admit (to others) that I am freezing"
From what I have understood so far I can say that, as a rule of thumb, "til" can be translated to "in order to". So your above sentence Det er umuligt til at forstå ... would translate to It is impossible in order to understand ...". Compare: In order to understand it, ..., which would translate to Til at forstå det, .... Another example: In order to get it, you ... which translates to Til at få det, du ...*
I believe in the example you give, at the beginning of a sentence, for should be used: "For at forstå...". In another sentence it might work with til but that would be determined by what is preceding it. I suppose the only way to find out if a certain construction works, without the help of native speakers, is to do a search for it or similar constructions. Ordnet.dk has the possibility to search for phrases and see how they are used in actual Danish texts: http://ordnet.dk/korpusdk/
In the following topics, Xneb gives some explanation of when the til is added in some cases and not others:
so apparently in cases as discussed here, as a rule of thumb: "After adjectives, pronouns and nouns til is added before the infinitive, whereas without a preposition, it normally follows an adverb or another verb."