My HS history teacher, who is a very smart man and a Democrat, met Bush personally and had a long conversation with him; he thought that Bush was highly intelligent and well-informed.
If you look at videos of Bush speaking publicly, you see that he frequently reads speeches from a paper copy on his lectern instead of a teleprompter, and is probably a bit nearsighted, so he pauses and/or stumbles over words frequently.
That, combined with the natural tendency to ascribe every negative quality to one's political opponents, and classist disdain for his "Good Ol' Boy" act,* was what caused the charges of "stupidity" on his part.
*Which probably hurt Democrats quite a bit; the caricature of Bill Clinton as "Bubba" by coastal Republicans had similar effects.
(GWB was of course perfectly capable of turning his act
on and
off as needed).
Bush is a poor public speaker, but he doesn't really want for IQ. Palin strikes me as 100 IQ at best.
Palin's teleprompter malfunctioned halfway through her universally-praised* 45-minute 2008 convention speech and she ad-libbed the rest without skipping a beat. That's not something that a person of average or below-average intelligence is capable of doing. Palin is probably around an IQ of 110 with a high verbal component. GWB I'd say is around 125.
*At the height of Palinmania, but it pretty much holds up.
Poll
