If you’re restricting to the class of “Boltzmann brains that understand the concept of Boltzmann brains”, then you are conditioning on something other than observations. All you can observe is that you believe that you understand Boltzmann brains.
The proportion of Boltzmann brains making that observation and being essentially correct in that belief will have so many zeroes after the decimal point that you easily could fill a set of encyclopedias with them and have more to spare.
It is difficult to convey how ridiculously uncorrelated Boltzmann brains would be if they could exist. Yes, with infinite time or space many of them will be able to have sensory experiences, memories, and thoughts. Some microscopic fraction of those would have memories about attending university and discussing quantum physics, and thoughts along the lines of “If I were a Boltzmann brain then …”.
The incomprehensibly vast majority of those will have no further thoughts at all, being dead or otherwise incapable of thought any more. Of those that do go on to have more thoughts, the incomprehensibly vast majority will have thoughts as sensible and human-like as “nYqR8pwckvOBE84fKJ8vPMUWR3eYEbO6nXyOuSC”. Of those that have any thoughts that we would recognize as vaguely human, the incomprehensibly vast majority will go on to continue in a manner less logically coherent than ”… a ten foot bull dyke shoots pineapples with a machinegun.”
So yes, if you were actually a Boltzmann brain then you could think you were an exception. But almost certainly, you would not. You would almost certainly not think anything even slightly related to your previous thoughts at all.
If you’re restricting to the class of “Boltzmann brains that understand the concept of Boltzmann brains”, then you are conditioning on something other than observations. All you can observe is that you believe that you understand Boltzmann brains.
The proportion of Boltzmann brains making that observation and being essentially correct in that belief will have so many zeroes after the decimal point that you easily could fill a set of encyclopedias with them and have more to spare.
It is difficult to convey how ridiculously uncorrelated Boltzmann brains would be if they could exist. Yes, with infinite time or space many of them will be able to have sensory experiences, memories, and thoughts. Some microscopic fraction of those would have memories about attending university and discussing quantum physics, and thoughts along the lines of “If I were a Boltzmann brain then …”.
The incomprehensibly vast majority of those will have no further thoughts at all, being dead or otherwise incapable of thought any more. Of those that do go on to have more thoughts, the incomprehensibly vast majority will have thoughts as sensible and human-like as “nYqR8pwckvOBE84fKJ8vPMUWR3eYEbO6nXyOuSC”. Of those that have any thoughts that we would recognize as vaguely human, the incomprehensibly vast majority will go on to continue in a manner less logically coherent than ”… a ten foot bull dyke shoots pineapples with a machinegun.”
So yes, if you were actually a Boltzmann brain then you could think you were an exception. But almost certainly, you would not. You would almost certainly not think anything even slightly related to your previous thoughts at all.