Differences between 知った and 知っていた

Question

There's this song from LiSA that I've been trying to understand the lyrics. However, there is something that is bothering me right at the start.

The first verse of the song reads as

強くなれる理由を知った

and it gets translated as (watch the video with subtitles on, at 1:05)

I've found a reason to become strong

Now, what's bothering me is that we normally use 知っている to say that we know something. So I was expecting to see 知っていた for "I knew/I've found".

I think I understand the dilemma of 知る vs 知っている in the present, the latter being a change of state (of not knowing to knowing) and hence the usage of ～ている. But what if the verb is in the past? What are the differences between 知った and 知っていた, and why is the former used in the lyrics?

Answer 1

As far as you are speaking in the affirmative, the verb 知る is like any other verb that describes an instantaneous change of state. The dictionary form refers to a change that either happens habitually or will happen in the future. It can be translated as “get to know” or “learn” The simple past form 知った only describes a change that happened in the past. It corresponds to “got to know” or “learned.” The English verb “know” is the one that is peculiar here as its simple past form “knew” can describe both a past state and a past change of state.

知っている refers to a current state where you “know” something. Technically speaking, this is a state that resulted from a past change of state, although you are not always conscious of what put you in that state or when that event happened. Similarly, its past version 知っていた describes a past state that, technically speaking, resulted from an earlier change of state. This corresponds to “knew” in its stative sense.

The peculiarity of the Japanese verb comes into play when you start talking in the negative. The simple negative form 知らない refers to a current state where you don’t know something, not a change of state that doesn’t or won’t happen. 知らなかった is used for a similar state in the past, not a change of state that didn’t happen. 知っていない and 知っていなかった are both ungrammatical and should never be used.

Answer 2

verb-た is not a past tense per se, it's the accomplished form. (That's why you can see it used for sentence speaking about the future.)

知った doesn't only mean "I knew", it means "before I didn't know, and after I knew." The fact of my knowing has been accomplished.
知っていた means I was in the knowing both before and after, there are no changes happening here.