>>Thoughts are actual things that occur.
Prayers are not proven to occur, help in any way, and get this.....are just thoughts.
So in all truth...."thoughts and prayers" are the same things.....
Would you like to participate in a prayer experiment with me?<<
Maybe I'm reading you incorrectly. The first two sentences seem to contradict each other.
What if I do not think that thoughts and prayers are the same thing? I pray verbally just like saying grace. I don't think out loud.
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Some thoughts are affirmations. When one chants in a group or say affirmations in a group, then it's easier to remember it and feel the positive energy from it.
If one thinks about someone else's problems, then they may think of something or do something to help them. For example, I can't help someone who lives with an alcoholic or has an alcohol addiction. Thoughts and prayers doesn't help in this situation, but maybe you know a professional or a group that can help so you steer them towards that. It may not be easy to convince somebody to get help, so the thoughts and prayers are for you to have the courage and fortitude for sticking your nose in, or for guidance on what to do. The answer to your prayer could say don't stick your nose in this situation, as well.
Thoughts may also be intuitive and are from God.
As for prayer, it's to ask God to help them in their time of grief, something positive to happen for them or that they stay safe and harm does not fall upon them.
I do agree that if I know someone is an atheist, then I would not say it no matter how sincere I would be. I don't want to insult their beliefs. I think that birds of a feather flock together and that your close friends are people you share common beliefs with. Not everyone can help directly, but they may chip in money or start up a gofundme for you.
As for saying it to feel good about oneself, i.e. being selfish, then it's not sincere. It's to make the other person feel good and that you're there for them. It's like apologizing and then not following up on it.