... that 2+2=11₃ ... how 'bout'choo?

Actually, the math illustration of 10x10=150 is not a good example of non-volitional belief. 10x10 is defined to be 100 ... in any base ... 10x10=100_{2, 3, 4, etc.} ... it's a mathematical tautology.

Perhaps a better example might be my belief that Obama is not a natural-born citizen and is thus ineligible to be President. The only thing that would change my belief is going to Hawaii and seeing an original long-form birth certificate signed and witnessed.

It is interesting that my belief was not formed in my subconscious ... and, yes, you might say it is non-volitional at this point, but I say that I made a choice and I see no reason to change my choice ... that's what choices are all about ... if you go to San Francisco to spend tomorrow, you can't go to Paris tomorrow ... but I have stated what would change my choice ... and you could decide to go to Paris tomorrow, but then you would not be able to go to San Francisco.