Forum:Betty and Bubblegum same person?

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I just had to check if anyone else was wondering this. Could Princess Bubblegum and Simon Petrikov's (the Ice King) fiance Betty be the same person? The original first name for PB was going to be Bettie. I know they changed it and I know it's a different spelling, but still it got me thinking. Betty and PB look fairly similar. If you made Betty pink, got rid of her glasses, and made her hair longer it would be an even closer resemblance. Betty's hair ends in the same little waves as PB's hair. I know that PB is supposed to be 18, but it's already been shown that her age is dependent on the amount of candy biomass she has and not the passage of time. Additionally, the Ice King got his powers and current appearance from the magical crown that he bought. What if a similar thing happened to PB? Her crown has been shown to be magical as well. The gem in both the Ice King's crown and PB's crown protected them from the Lich's mind controling effect, showing that the two magical artifacts might be related. It has also been shown that PB is not like the other candy people since she doesn't explode when scared. She created the Earl of Lemongarb, meaning that it is possible she created the other candy people as well. PB is a scientist, and Betty was shown to be a scientist of some sort. Betty is wearing a lab coat in one of the pictures that the Ice King had of her during his transformation. Lastly, this would explain the Ice King's obsession with capturing her the most over the other princesses and marrying her, since subconsciously he believes her to be his lost fiance. Maybe I'm imagining it, but the more I think about it the more it makes sense. Does anyone know if PB's original name Bettie was written or was it said verbally, meaning that the spelling might have been intended to be Betty but whoever wrote it down first changed it? Anyway, what do you all think?