I don't know why I love you, even when you are homeless.
I don't know as to why I love you, even when you are homeless.
I am crazy because I don't know what the difference between these two sentences is.
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Let’s break it down. “As to” is synonymous with “regarding”, “concerning” or “with respect to”. In a real use case (news headline):
Here's A Quick Explanation As To Why Today's Jobs Number Made No Sense
It doesn’t add much meaning in “as to why” compared to “why”, except for sounding more pedantic.
as to (preposition)
1 : as for, about
2 : according to, by
Your example sentence with "as to" doesn't make much sense to me.
I would rather use "regarding" or "concerning" unless there is a transition. When used in "as to why, how whether" etc., it is often better to drop "as to" and simply use why, how, whether. For example,
I don't understand as to why you are going there.
I don't know as to how to drive a bike.
I don't know as to whether you'd like it.
should simply be
I don't understand why you are going there.
I don't know how to drive a bike.
I don't know whether you'd like it.
But, in the following, where you see a transition, "as to" is used to reflect that.
I like English language. As to why I do, I really don't know. (=...but if you want to ask why I do, I don't know.)
I am going for sure. As to whether Jane will go along too, you will have to ask her yourself.
English is fun, as to math, forget it. (contrast)
John and Mary fought over small things all the time, things that you and I most likely won't give a damn. As to why they do, it is beyond me.