It appears the one of the definitions of prayer is "an honest hope or wish." As long as this hopeful or wishful thought is not directed at some god or universal consciousness, with the expectation of it being heard in some way, then I suppose an atheist can "pray."

Prayer, as generally taught, takes one of two forms: meditative / surrender (not my will, but thine be done) or petitions.

Most people seem more interested in the petitioning prayer -- to obtain grace of some sort, such as finding a parking space or asking for a miraculous cure (both the ridiculous and the sublime, you might say). By definition, an atheist has no divine being to direct such a prayer to, so that is inherently impossible. I personally don't see this as a loss, since when I was a believer, petitioning prayer never worked anyway. Besides, it's not even a coherent concept.

An atheist also has no one to surrender their will to, or to sooth themselves by imagining such a being to be "in control" in some benign manner. So I can't see how meditative prayer would work, either.

Some atheists I've known practice secular meditation -- but that is not really prayer as it isn't addressed to or focused on a deity, but on something innocuous, like a spot on the wall, or one's breath. One can obtain benefits from this -- reduced anxiety, mainly -- and since I'm not a particularly anxious person I have not really seen much use for it. Other's mileage can (and does) vary.

Now if one just means prayer to be wishing or hoping for something, I suppose we all try to will the damned universe to cooperate with us at times. It's only human. And in my experience as a former believer, an awful lot of prayer is just that, decorated with religious ideation.

I think we call it meditating.

I remember when I was a child and got dragged to different churches I never got the hang of it. I guess prayers were the precursors of mobile phones but with a shitty plan. A sort of lifelong subscription with no connection guarantee.

Why would an atheist want to pray and to whom or what?.

The author is a member of the Unitarian church which has the following object :-

To promote a free and inquiring religion through the worship of God and the celebration of life; the service of humanity and respect for all creation; and the upholding of the liberal Christian tradition.

Doesn't sound much like an atheist to me.

"communicating with the Holy outside" … What? the holy shit?

What the heck???

What would I be praying to and why?

This is all a matter of definition of the word prayer. The dictionary gives two definitions....one is “a solemn request for help or thanks to a deity or god”...obviously that is nonsensical if one is atheist. The second definition is ...”an earnest hope or wish”, one which everyone can identify with, theist and non theist alike.