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For what it's worth they cite Jewish laws. From the brief [emphasis mine]:

The relevant passages from the Talmud demonstrate that the rabbis sought -- with the scientific knowledge and means available to them in their time -- to formulate the quickest, least painful, and least disfiguring methods of execution that the technology of the day would allow within the framework of Biblical texts.

Then they list the 4 acceptable forms of punishment, of which one is "stoning". To that end they write,

A. "Stoning" Was Intended To Be a Quick and Relatively Painless Form of Non-disfiguring Execution.
The Mishna in tractate Sanhedrin (45a) describes execution by "stoning." The condemned defendant was pushed from a platform set high enough above a stone floor that his fall would probably result in instantaneous death. [emphasis mine, citation omitted]

Yet the Bible states otherwise,

[KJV] Numbers 15:
35 And the LORD said unto Moses, The man shall be surely put to death: all the congregation shall stone him with stones without the camp.
36 And all the congregation brought him without the camp, and stoned him with stones, and he died; as the LORD commanded Moses.

It doesn't say anything about building a platform and PUSHING the guilty party off.

Finally, they conclude,

If execution by the electric chair, as administered in Florida, results in unnecessary pain and disfigurement, it would be unacceptable under the principles underlying the traditional Jewish legal system applied 2000 years ago, and should also be unacceptable under the Eighth Amendment today.

Bouvier's Law Dictionary, Rev. 6th ed. (1856) notes that, '[t]o attain their social end, punishments should be exemplary, or capable of intimidating those who might be tempted to imitate the guilty.' Electrocution certainly fits that definition. Capital punishment is just that - punishment - not a pat on the back.

Just thought it weird the court would even accept it. It was a first. No U.S. law or precedent cited. What is next? We going to have Jerry Falwell submit briefs based on St. Paul's Epistle to the Romans and Baba Ram Das submit them based on the Brhadaranyaka?

Oh wait..we won't have to worry about Falwell. Armed guards will take him away because the ACLU will have an injunction ready for him when he walks in the door. We might have to worry about Baba Ram Das however.