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As for the distress response at the centre of this study, Inzlicht says the effect holds even when God isn't top of mind.
"Regardless whether you're thinking about it or not, you tend to show this effect, though it does seem to magnify when you are thinking about it."
So he's saying that believers show less stress when they make mistakes vs non-believers.
But:
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"And to the extent that we want to make fewer errors in our life, having anxiety about making errors is adaptive," he said. "Because the more anxious you are about making an error, the less likely you are, in theory, to make an error in the future."
So non-belief is adaptive and should dominate over time.
Buddhist meditators will show the same response, tho not just about mistakes, but greater calmness in general, and they don't intentionally think about God at all.