Alex left his Spiritual sea that had given him quite the surprise this time, and moved on to checking other aspects of his body.
Since his Intent hadn't increased just yet, he didn't expect his Sword Intent to have grown much further either. He had reached the point he needed to start learning his Sword Heart, and since he had no memory of anything in between during the 50 or so years that had passed, the chances that he had come up with a Sword Heart were low as well.
Depending on whether or not he knew he would lose his memories upon leaving that place — which they believed to be the Realm within Realms — he could have just not done a few certain things, such as deciding upon his Sword Heart.
It made no sense for him to have decided on something to be his Sword Heart if he was going to forget about it soon after. Besides, he had cultivated in that time and eaten the two other fruits from the Tree of Life, which should have accounted for most of his time that he had lost.
