Todas as indicações são de que o médico
started each cycle in the same state: believing that he had arrived, for the first time, directly from Earth. Every time he noted the passage of time from his reading of the stars, he had the same expression of confusion or disbelief. He had to rediscover his surroundings each time.
Existe um sentido em que
his true age is in the billions of years: the cumulative copies of him did toil away for all that time. He is aware of this fact; however, the knowledge is not first-hand. From chronological aging of his body and first hand experience, he is exactly one cycle older then when was he teleported to the castle for the first time.
Tudo isso, é claro, está sujeito a revelações contraditórias, mas não houve nada no episódio que indique claramente o contrário.