I once believed that six times one is one.

I don't remember how it came up in conversation, but for whatever reason numbers became relevant and I clearly and directly stated my false belief. It was late, we were driving back from a long hard chess tournament, and I evidently wasn't thinking clearly. I said the words "because of course six times one is one." Everyone thought for a second and someone said "no it's not." Predictable reactions occurred from there.

The reason I like the anecdote is because I reacted exactly the same way I would today if someone corrected me when I said that six times one is six. I thought the person who corrected me must be joking; he knows math and couldn't possibly be wrong about something that obvious. A second person said that he's definitely not joking. I thought back to the sequences, specifically the thing about evidence to convince me I'm wrong about basic arithmetic. I ran through some math terminology in my head: of course six times one is one; any number times one is one. That's what a multiplicative identity means. In my head, it was absolutely clear that 6x1=1, this is required for what I know of math to fit together, and anything else is completely logically impossible.

It probably took a good fifteen seconds from me being called out on it before I got appropriately embarrassed.

This anecdote is now my favorite example of the important lesson that from the inside, being wrong feels exactly like being right.