The entire business concerning prayer in schools and elsewhere rests on the presumption that the law can discern prayer and distinguish it from all other activities. I deny this. The law makes no claim concerning the existence of a deity. In the absence of the belief in a deity, praying cannot be distinguished from another form of discourse, namely, talking to oneself. Even supposing the subject addresses the deity by name, an agnostic law cannot make the case that the subject is praying, as distinguished from talking to himself, without conceding the existence of that deity, which seems to give up the main point.
Now, this is more than a mere sophistry. It points to an area where the justice system is unfit to make a judgment. This used to be referred to as ultra vires, beyond the powers, of the court. Neither the term nor the idea is used much anymore, as the domain ultra vires has shrunk almost to invisibility in recent decades.
If the law cannot definitively discern the act of praying, then surely the law cannot be interpreted as forbidding the appearance of praying. If the court were to rule against talking to oneself, every doddering old man or pocket-protector computer geek (and I am both) would be in danger.