Who are you, baby?

"I think therefore I am", said the much-admired French thinker Rene Descartes. But he could have said "I feel therefore I am", and avoided narrowing the focus of fellow philosophers ever since.
At the risk of sounding like a mystic, he could have simply saying that "I am", without focusing on any one particular sense. That would have been enough.
Or even more illuminating by remarking that "I notice that there is a thought and a thinker who is having the thought" and he could have got game set and match if he had noticed that there is not only a thought and a thoughtholder but there is also someone or something who is noticing the process. That's you, baby.