! As we learned in DR2: Chapter 0, Izuru is obsessed with the concept of unpredictability; his entire character arc is defined by this and everything Izuru has done to this point has been to find something he, even with his ultimate analytical abilities cannot predict.
! Izuru's first attempt to find unpredictability is with Junko and her despair. When he first meets her, Izuru is convinced that life is meaningless and there nothing he cannot understand and predict. The only reason he ultimately agrees to give Junko's beloved despair a try is the notion that Despair is unpredictable; not fully acquainted with Despair, Izuru decides helping Junko might be a way to find something that brings meaning to his dull existence. At first, Izuru finds a minor bits of excitement in 'despair' when, contrary to his expectations, a bullets manages to scratch his cheek in the First Mutual Killing; for the first time, Izuru found something 'unpredictable'. It is this that ultimately convinces Izuru to aid Junko in her pursuit of Despair; not long after though, Izuru comes to find even Despair predictable (Why? I'm not sure. Right now I'm just going to blame Izuru's powers). While watching Mukuro despairify Chisa, Izuru expresses that the scene in front of him was 'boring'. With this one phrase, it can be gleaned that Izuru now finds despair boring, something Junko herself could not grasp.
! Izuru's ability to predict the 'unpredictable' leaves Izuru in a constant state of self-deprecation: as there is nothing he cannot predict in the world of people, even something as chaotic as despair, over the courses of the next three years, he eventually turned to the flow nature to satisfy his appetite for the 'unpredictable'. And even then, after focusing one aspect of nature for a short period of time, it would become meaningless. When Izuru is aboard the ship approaching Jabberwock, he monologues that he likes how unpredictable the bobbing of the ship is; in fact, he is so enamored in such a seemingly trivial thing matter that he isn't even fully aware he's on a ship. He only becomes cognizant of this reality when Nagito disturbs his trance by bothering Izuru with a conversation that unsurprisingly, Izuru finds boring. It should be noted that during the monologue, Izuru states that eventually, he would probably find the bobbing he was so intently focused on dull and meaningless, just like he does with everything else.
! Unlike Junko, whose analytical abilities, while great, prevent her from deciphering more random parts of reality (which is why she loves despair), Izuru capabilities for prediction are endless, to an absurd degree. Nothing in the world can pique his interest for more than a fleeting moment, because, as soon as he gives even completely random events, like the flow of the ocean, a little thought, any sort unpredictability he thought he could find in such things disappears.
! Before I end this analysis on Izuru's search for the unpredictable, I want to bring up one thing Izuru said that I found interesting (thanks to reddit), something that would probably just be seen as throwaway, had it not be Izuru saying it: specifically, Izuru asking Chiaki "Who are you?". I should point out that in all of his introductions to other characters, Izuru has never been the one to ask who the other person is, because, I would assume, if I my character analysis is correct, that he has never discovered another person that piqued his interest in his slightest, that he couldn't predict, and was worth knowing. To qualify this, I will bring up the other two character introductions that Izuru was fully involved in: when he meets Junko and Nagito. In Junko's case, she forced herself in his face until he would listen on her spiel on Despair; this scene made it very clear, to me at least, that Izuru had no interest in Junko herself, just concept of Despair; the fact Izuru showed no interested in Junko until she brings up despair confirms this. When he was talking to Nagito on the boat in DR2: Chapter 0, things weren't much different. Nagito was just a pest keeping Izuru away from his focus on the bobbing of the boat. The only reason Izuru keeps his conversation with Nagito going is that he realizes that Nagito has a direct relation to Junko, and once he scrounges all the information of Nagito that he wants, Izuru has already begun to view him as useless as everything else. The reason why Izuru's "Who are you?" to Chiaki is so poignant is because its the first time Izuru express interest in an individual and not the ideas they were trying to share.
! Now, to discuss the possible implications behind this inquisition of Izuru's:
! 1) Chiaki herself actually sparked a feeling of interest and meaning to him.
! I'm not sure about this. Maybe he does have residual memories regarding his past life, specifically about Chiaki, but I don't know. I mean, personally, I'm all for 'the power of love and hope' overcoming the nihilism of Izuru's existence, because, shit, things are really bleak in this series, and we could use some happiness, but personally, I think Izuru's interest in Chiaki has a more logical reason behind it. Specifically…..
! 2) Chiaki's words implied to Izuru that he wasn't always some god tier, super analyst, and he's curious about his previous self. He wants to know more about the person he was before he became the emotionless shell he currently is
! In other words, I'm saying Izuru is interested in the notion of his previous life and wonders if Chiaki, someone who seems to know the person he was before, knows about him. If he gets to know Chiaki, maybe he can learn about a way his previous self and maybe he can find a way to satiate his appetite for unpredictability through that. Maybe he thinks that by understanding his past self, he might be able to ignite some spice in his life.
! That's about all I have to say. I guess one important thing I should mention before concluding this is that Izuru never fell into despair. He obviously began to grow weary and bored of it during Chisa's torture scene, and, maybe (probably), went off to do his own thing following Junko's takeover.
! I'm also really curious as to why he uploaded Junko's AI to the Hope Restoration Program. That will probably be answered in the next few episode, but I guess I'll wait.
Sorry for this long post. But if you managed to stomach it, please discuss.