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The Van Pelt – Nanzen Kills A Cat Lyrics 15 years ago
This is actually based on a Zen Buddhist teaching story by the same name.
The gist of the story is as follows:

In the temple, there is a master who has achieved enlightenment.
His disciples pester him regularly with questions, hoping that they may too achieve the same goal.
Frustrated by the lack of progress in his disciples, Nanzen proclaims "If no one can answer me this question, I will kill this cat. What is the nature of the Buddha?" Being as the cat was a favored cat around the temple, and it was much loved, the students tried to answer the question. Though they spoke many answers, none satisfied the master, and so he took a sickle to the poor cat. The disciples sat horrified. Just then, the wisest student returned from his journey, removing his shoes at the door. The master asked again, "what is the nature of the Buddha?", and the wisest student, without hesitation, picked up his shoes and placed them on his head. To this the master replied, "Ah, if only you had been here sooner, this cat could have been spared."

The purpose of stories like this one was to confuse the readers. While pondering what the story could actually mean, they would ultimately draw a blank, completely at a loss for any explanation. That blankness of the mind was, according to Zen Buddhists, a preview of what enlightenment is.

Zen Buddhists are very mistrustful of words and language, and feel that nothing can be taught by them.
In addition, the "nothing" of which the song speaks is likely speaking of Nirvana, or enlightenment, which is effectively nothing, or a state of nothing. You'll have to do more research on Buddhism to understand that.

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